Calculus
Limits, derivatives, optimization, and behavior of functions.
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find the derivative of f(x) = 9e^x + x^5. f(x) =
$9e^{x}+5x^{4}$
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hw_2.1_basic derivative rules due sep 14, 2025 11:59 pm. 9. submit answ…
$4e^{x}$
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attempt 1: 10 attempts remaining. use the rules of derivatives to calcu…
$\frac{5}{x}$
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9. submit answer practice similar x - coordinate(s) of absolute maximum…
x - coordinate(s) of absolute maximum: None x - coordinate(s) of absolute minimum: 2.5 x - coordinate(s) of relative maxima: None x - coordinate(s) of relative minima: 2.5
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attempt 1: 10 attempts remaining. evaluate $\frac{d}{dt}(5e^{- 12t})$. …
\(-60e^{-12t}\)
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consider the function (f(x)=81x^{1/3}-3x) over the domain (0,140). a) l…
a) Critical values: $x = 0,x = 27$; Classification: $x = 0$ is a relative minimum, $x = 27$ is a relative maximum. b) relative minimum
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what is one limitation of federal government initiatives to address eco…
They do not address systemic barriers or root causes of poverty.
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1. submit answer practice similar attempt 1: 10 attempts remaining. whi…
B. It increases rapidly and is always above the $x$-axis.
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4. information about a function g(x) is given in the table. the functio…
$-\frac{3}{2}$
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suppose that the cost, in dollars, for a company to produce $x$ pairs o…
a. $C'(x)=5 + 0.02x+0.0006x^{2}$ b. $C'(100)=13.00$ dollars/pair c. $C(100)=7600.00$ dollars
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suppose that the cost (in dollars) for a company to produce x pairs of …
(a) $C^\prime(x)=3 + 0.02x+0.0006x^{2}$ (b) $C^\prime(100)=11$
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find the exact location of the relative and absolute extrema of the fun…
Relative maximum at \((2,35)\) Relative minimum at \((-2,-29)\) Absolute maximum at \((-5,133)\) Absolute minimum at \((5,-127)\)
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hw_2.1_basic derivative rules due sunday by 11:59pm points 100.05 submi…
$0.13$
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what is one limitation of state government initiatives to address econo…
State governments cannot adjust the federal minimum wage that was set in 2009.
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attempt 1: 10 attempts remaining. let $p(x)=5sqrt{x}+0.75x^{2}$. a. fin…
a. $P^{\prime}(x)=\frac{5}{2\sqrt{x}} + 1.5x$ b. $\frac{P^{\prime}(x)}{x}=\frac{5}{2x^{\frac{3}{2}}}+1.5$
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the population of a city is modeled by the equation (p(t)=230,000 + 700…
7000
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13. the average monthly cell phone bill in a given year for a us consum…
a. $B^\prime(t)=0.46t - 0.05$ b. The average monthly cell phone bill is increasing by $\$4.55$ per year.
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the distance, s (in feet), traveled by a car moving in a straight line …
a. $s^\prime(t)=8t - 2$ b. $s^\prime(3)=22$
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based on data from 1940 to 2000, the average yearly social security ben…
a. $S'(t)=0.696t - 5.5$ b. The average yearly Social Security Benefits are increasing by $8.42$ thousand dollars per year in 1960.
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for 0 ≤ t ≤ 4, the average price of a home in a city is modeled by the …
a. $p^\prime(t)=2.6t - 12$ b. $p^\prime(2)=-6.8$
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attempt 1: 10 attempts remaining. for 0 ≤ t ≤ 4, the average price of a…
a. $p^\prime(t)=2.6t - 12$ b. $p^\prime(2)=-6.8$
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the amount of water passing through a particular dam in a day is given …
a. $\frac{df}{dt}=-7t + 78$ b. $-132$
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acme manufactures screws using labor and equipment. its total daily cos…
17
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hw_2.1_basic derivative rules due sunday by 11:59pm points 100.05 hw_2.…
$g'(u)=\sqrt{7}+\frac{\sqrt{6}}{2\sqrt{u}}$
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1. differentiate $f(x)=\frac{x^{2}-4x + 1}{x^{2}}$. answer: $\frac{df}{…
$\frac{4}{x^{2}}-\frac{2}{x^{3}}$
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find $f(a), f(a + h)$, and the difference quotient $\frac{f(a + h)-f(a)…
\(\frac{-24}{(a + h-8)(a - 8)}\)
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the function (f(x)= - 4x^{3}-18x^{2}+120x - 8) is increasing on the int…
The function has a relative maximum at \(x = 2\). It is decreasing on the interval \((-\infty,-5)\) and the interval \((2,\infty)\). It is increasing on the interval \((-5,2)\).
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1.4 assignment part 1 90% credit until: september 19 at 8:00 am complet…
\((-1,2)\) and \((5,\infty)\)
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determine all intervals on which the graph of f is decreasing. graph of…
\((-5,-2)\), \((1,3)\), \((4,\infty)\)
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find an equation of the tangent line to the give curve at the point (2,…
\(y - 1=m(x - 2)\) (where \(m\) is the slope of the tangent line at the point \((2,1)\) obtained by differentiating the curve equation and substituting \(x = 2,y = 1\))
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attempt 1: 10 attempts remaining. let (f(x)=x^{7}-3x^{5}+7x^{3}-3x - 3)…
$f^\prime(x)=7x^{6}-15x^{4}+21x^{2}-3$ $f^\prime(2)=289$ $f^{\prime\prime}(x)=42x^{5}-60x^{3}+42x$ $f^{\prime\prime}(2)=948$
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attempt 1: 10 attempts remaining. let $f(x)=x^{4}+5x^{3}+2x^{2}+2x$. $f…
$f^\prime(x)=4x^{3}+15x^{2}+4x + 2$ $f^\prime(2)=102$ $f^{\prime\prime}(x)=12x^{2}+30x + 4$ $f^{\prime\prime}(2)=112$
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attempt 1: 10 attempts remaining. find $f(a)$ for $f(x)=-2 + 8x-7x^{2}$…
$8 - 14a$
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consider the following. 9x^2 - y^5 = 8 (a) find y by implicit different…
(a) $\frac{18x}{5y^{4}}$ (b) $\frac{18x}{5y^{4}}$ (c) $\frac{18x}{5y^{4}}$
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attempt 1: 10 attempts remaining. for which values of $x$ does the grap…
$x=-3.0000,x = 3.0000$
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let (f(x)=-4x^{2}-20x + 2). find the (x)-value(s) where the graph of th…
$x =-\frac{5}{2}$
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attempt 1: 10 attempts remaining. use the rules of derivatives to calcu…
$-5x^{24}+\frac{1}{2\sqrt{x}}$
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use the rules of derivatives to calculate the derivative of the followi…
$9+\frac{4}{3}x^{\frac{1}{3}}$
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17. let $f(x)=5x^{1/5}-4x^{5/7}$. evaluate each of the following: 1. $f…
1. $-\frac{13}{7}$ 2. $\frac{1}{4^{\frac{4}{5}}}-\frac{20}{7\times4^{\frac{2}{7}}}$
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differentiate $f(t)=\frac{1}{2}t^{6}-8t^{4}+t$. answer: $f(t)=$
$3t^{5}-32t^{3}+1$
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hw_2.1_basic derivative rules due sunday by 11:59pm points 100.05 hw_2.…
$2x - 6$
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14. if $f(x)=\frac{3}{x^{2}}$, find $f(4)$.
$-\frac{3}{32}$
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hw_2.1_basic derivative rules due sunday by 11:59pm points 100.05 submi…
$-\frac{90}{x^{7}}$
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hw_2.1_basic derivative rules due sunday by 11:59pm points 100.05 submi…
$\frac{15}{2}t^{-\frac{7}{4}}$
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attempt 1: 10 attempts remaining. use the rules of derivatives to calcu…
$-42t^{5}$
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hw_2.1_basic derivative rules 9. submit answer practice similar attempt…
$-\frac{2}{5}x^{-\frac{7}{5}}$
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attempt 1: 10 attempts remaining. use the rules of derivatives to calcu…
$8x^{7}$
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attempt 4: 7 attempts remaining. use the rules of derivatives to calcul…
$7$
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the graph of a function is given. (a) find all the local maximum and mi…
(a) local maximum $(x,y)=( \text{value from graph}, \text{corresponding y - value})$ (smaller x - value) local maximum $(x,y)=( \text{value from graph}, \text{corresponding y - va…
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if a rock is thrown from the ground with an initial velocity of 120 ft/…
(a) $v(t)=120 - 32t$ (b) $t = 3.75$ (c) $225$ (d) $a(t)=-32$
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this is section 2.5 problem 56: find the points on the curve f(x)=2x^3 …
$(0,5)$ and $(1,4)$
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the constitution was inspired by the english bill of rights. which of t…
limited power of the executive branch
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this is section 2.5 problem 44: for the function f(x)=x^2 - \\frac{1}{x…
$y=3x - 3$
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this is section 2.5 problem 44: for the function f(x)=x^2 - \\frac{1}{x…
$y=\frac{17}{4}x - 5$
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question 20 · 1 point given the function of ( f(x)=7x^{1/2}-3 ) on the …
\(20.25\)
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question 19 - 1 point find the absolute maximum and absolute minimum of…
Absolute maximum of $43$ at $x = 4$, Absolute minimum of $-5.38$ at $x = 0.6$
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question 18 · 1 point find (dy) and evaluate when (x = - 2) and (dx = 0…
$-\frac{121}{40}$
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question 17 · 1 point find the critical points of the function f(x)= - …
$\frac{\pi}{2},\pi,\frac{3\pi}{2}$
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question 16 - 1 point if a brick is dropped from a height of 81 ft, its…
$\frac{9}{4}$
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question 15 · 1 point the radius of a circle increases at a rate of 6 m…
$108\pi$
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this is section 2.5 problem 44: for the function f(x)=x^2 - \\frac{1}{x…
$y=-x + 1$
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question 13 · 1 point find the derivative of $f(x)=4x^{-2}cdotln(x^{4}-…
$-\frac{8\ln(x^{4}-3x)}{x^{3}}+\frac{4(4x^{3}-3)}{x^{2}(x^{4}-3x)}$
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question 12 · 1 point let y be defined implicitly by the equation (8x +…
\(\frac{27x^2 - 24(8x + 3y)^2}{9(8x + 3y)^2+6y}\)
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question 10 · 1 point find the derivative of (h(x)= - 3cos^{13}(x)). pr…
$39\sin(x)\cos^{12}(x)$
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8. if n(x) is a continuous function, how many roots are guaranteed by t…
3
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question 7 · 1 point a particle travels along a horizontal line accordi…
$12t^{2}-42t - 4$
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question 6 · 1 point find $\frac{d}{dx}(-4x^{1/4}-5x^{-3/4})$. provide …
$-x^{-3/4}+\frac{15}{4}x^{-7/4}$
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7. what is the horizontal asymptote of the function $m(x)=\frac{x^{2}+l…
$y = 0$
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sample response: i would apply for several scholarships and grants so t…
scholarships and grants loans work - study
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5. the graph of a function f is shown in the figure above. which of the…
C. $f^{\prime}(b)$ exists.
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question 6 · 1 point find $\frac{d}{dx}(-4x^{\frac{1}{4}} - 5x^{-\frac{…
$-x^{-\frac{3}{4}}+\frac{15}{4}x^{-\frac{7}{4}}$
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question 5 · 1 point find $\frac{d}{dx}(-x^{-1}+5x^{-4}+3)$. provide yo…
$x^{-2}-20x^{-5}$
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4. for what value of k is $h(x)=\begin{cases}kx^{2}-6&x < 2\\4x + 10&xg…
$k = 6$
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question 3 · 1 point find slope of the line tangent to the graph of f(x…
$5$
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practice answer these questions. 1. analyze what does the preamble to t…
1. It was created to secure fundamental rights and liberties, limit government power, and ensure a just and free society. 2. It indicates a formal decision or determination. 3. It…
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question 3 · 1 point find slope of the line tangent to the graph of f(x…
$5$
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consider the graph of y = f(x) shown below in blue. find the open inter…
$(0,\infty)$
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2. if $f(x)=\begin{cases}x^{2}+3, & x eq1\\1, & x = 1end{cases}$, then …
D. 4
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name two important concepts found in the magna carta.
1. Limited royal power 2. Due - process
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which of the following sets most accurately matches the important docum…
C. Mayflower Compact: self - government, representative democracy
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question 5 of 5 to manage my diabetes, i need prescriptions and medical…
A. HealingRx: Has a wide list of prescriptions, including insulin, and covers 50% of needed medical devices.
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how did the english bill of rights limit the power of the english monar…
It restricted law - making, tax - levying, army - maintaining powers and gave rights to Parliament.
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how does the detail in bold develop the main idea? when dr. james naism…
It describes a shift in attitude toward the jump shot.
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read the passage: the jump shot: a game - changing move when dr. james …
Because innovators like John Cooper challenged the conventions of basketball, the jump shot became a popular move.
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why does scarcity exist? * voluntary trade has benefits for both partie…
Resources are limited, but people's wants are unlimited.
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question 3 of 6 (4 points) | question attempt: 3 of unlimited distance …
(a) 0 miles (b) 75 miles (c) 75 miles
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concept vocabulary why these words? these concept vocabulary words sugg…
1. Sentence for "exercise": The citizens exercised their right to vote. Synonym: utilize. Impact on meaning: Similar meaning, more formal. 2. Sentence for "petition": The group fi…
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lim_{x\\to - 4^{-}}\\frac{1}{(x + 4)^{2}}= lim_{x\\to - 4^{+}}\\frac{1}…
$+\infty$
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erpret close read practice completing the reading sections of standardi…
1. D. be entitled to. 2. A. The Constitution defines some of our rights, but not every right.
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economics is a. the study of how limited resources are allocated to sat…
A. the study of how limited resources are allocated to satisfy unlimited wants
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why does scarcity exist? * 1pt voluntary trade has benefits for both pa…
1. Resources are limited, but people’s wants are unlimited. 2. Producers and consumers. 3. both people believe they are benefiting
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in a students calculus class, the final grade is based on four categori…
$80.86$
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the graph of the function f(x) is shown below. state all values of x in…
$x=-7, x = 2$
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21. modeling real life miami - dade county issues tickets for speeding …
The step - function is \(y=\begin{cases} 151, &0\leq x\leq9\\ 226, &9<x\leq14\\ 276, &14<x\leq19\\ 301, &19<x\leq29\\ 376, &x > 29 \end{cases}\) and the graph is as described abov…
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question how did the womens movement in the 1890s both expand freedom a…
C. Women won a degree of economic and political reforms, but they acquiesced in being defined as weak and dependent.
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use the figure to find the indicated derivatives, if they exist. (if an…
$-\frac{5}{12}$
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the graph of a function f is given. use the graph to find each of the f…
A. The function f has (a) relative maxima(maximum) at $2,4$ and the relative maxima(maximum) are(is) $5,5$
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use the graph to determine a. open intervals on which the function is i…
a. B. There is no interval on which the function is increasing. b. The function is decreasing on the interval \((-1,\infty)\) c. The function is constant on the interval \((-\inft…
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find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{…
2
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find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{…
\(2x+h - 9\)