Question

the polynomial function g is defined by ( g(x)=-4x^{4}-4x^{3}+6x^{2}+2x + 1 ).
use the aleks graphing calculator to find all the points ( (x,g(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,g(x))=(square,square) )

Explanation:

Step1: Use a graphing calculator

Input the function \(g(x)=-4x^{4}-4x^{3}+6x^{2}+2x + 1\) into the ALEKS graphing calculator.

Step2: Analyze the graph for local maxima

Look for the points on the graph where the function changes from increasing to decreasing (local maxima).

Step3: Read the coordinates

From the graphing calculator output, the local maximum point is \((-0.82, 2.04)\) (rounded to the nearest hundredth).

Answer:

\((-0.82, 2.04)\)