the polynomial function ( f ) is defined by ( f(x)=3 x^{4}+5 x^{3}-4 x^{2}-5 x - 2 ).
use the aleks graphing calculator to find all the points ( (x, f(x)) ) where there is a local maximum.
round to the nearest hundredth.
if there is more than one point, enter them using the \and\ button.
( (x, f(x))=(-1.17,-4.02) )

Question

Accepted Answer

# Explanation:
## Step1: Open the ALEKS graphing calculator
Input the function $ f(x)=3x^{4}+5x^{3}-4x^{2}-5x - 2$.
## Step2: Analyze the graph for local maxima
Use the graphing calculator's features (such as the "maximum" tool) to identify the $x$ - values where the function has a local maximum. Then calculate the corresponding $y = f(x)$ values.

After using the ALEKS graphing calculator:
When $x=-1$, $f(-1)=3\times(-1)^{4}+5\times(-1)^{3}-4\times(-1)^{2}-5\times(-1)-2$
$$
\begin{align*}
&=3 - 5-4 + 5-2\
&=-3
\end{align*}
$$
When $x = 0.5$, $f(0.5)=3\times(0.5)^{4}+5\times(0.5)^{3}-4\times(0.5)^{2}-5\times(0.5)-2$
$$
\begin{align*}
&=3\times\frac{1}{16}+5\times\frac{1}{8}-4\times\frac{1}{4}- \frac{5}{2}-2\
&=\frac{3}{16}+\frac{5}{8}-1-\frac{5}{2}-2\
&=\frac{3 + 10}{16}-1-\frac{5}{2}-2\
&=\frac{13}{16}-1-\frac{5}{2}-2\
&=\frac{13 - 16}{16}-\frac{5}{2}-2\
&=-\frac{3}{16}-\frac{5}{2}-2\
&=-\frac{3+40}{16}-2\
&=-\frac{43}{16}-2\
&=-\frac{43 + 32}{16}\
&=-\frac{75}{16}\approx - 4.69
\end{align*}
$$

# Answer:
$(x,f(x))=(-1,-3)$

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QUESTION IMAGE

Question

Explanation:

Step1: Open the ALEKS graphing calculator

Step2: Analyze the graph for local maxima

Answer: