the polynomial function ( f ) is defined by ( f(x)=3x^{4}+5x^{3}-4x^{2}-5x - 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))=(square,square) )

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Accepted Answer

# Explanation:
## Step1: Graph the function
Use the ALEKS graphing calculator to plot $ y = 3x^{4}+5x^{3}-4x^{2}-5x - 2$.
## Step2: Identify local maxima
A local maximum is a point where the function changes from increasing to decreasing. By observing the graph of the polynomial function $y = 3x^{4}+5x^{3}-4x^{2}-5x - 2$ on the graphing calculator:
The $x$ - coordinate of the local maximum is found by looking at the peak of the relevant part of the graph. After using the graphing - calculator's features (such as the "maximum" function in the graphing utility), we find that $x\approx - 1.17$.
Substitute $x=-1.17$ into the function $f(x)=3x^{4}+5x^{3}-4x^{2}-5x - 2$:
$$
\begin{align*}
f(-1.17)&=3(-1.17)^{4}+5(-1.17)^{3}-4(-1.17)^{2}-5(-1.17)-2\
&=3\times(1.17)^{4}-5\times(1.17)^{3}-4\times(1.17)^{2}+5\times1.17 - 2\
\end{align*}
$$
$(1.17)^{4}=1.17\times1.17\times1.17\times1.17\approx1.87$, $(1.17)^{3}=1.17\times1.17\times1.17\approx1.60$, $(1.17)^{2}=1.37$
$$
\begin{align*}
f(-1.17)&=3\times1.87-5\times1.60 - 4\times1.37+5\times1.17-2\
&=5.61-8.0 - 5.48 + 5.85-2\
&=(5.61 + 5.85)-(8.0 + 5.48+2)\
&=11.46 - 15.48\
&=- 4.02
\end{align*}
$$

# Answer:
$(x,f(x))=(-1.17,-4.02)$

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Question

Explanation:

Step1: Graph the function

Step2: Identify local maxima

Answer: