Question

the polynomial function h is defined by h(x)=x^4 - 3x^3 - 2x^2 + 4x + 5. use the aleks graphing calculator to find all the points (x, h(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, h(x))=(0.47, 5.92)

Explanation:

Step1: Recall local - maximum concept

Local maximum occurs where the function changes from increasing to decreasing. For a polynomial function \(h(x)=x^{4}-3x^{3}-2x^{2}+4x + 5\), we can use a graphing calculator (like ALEKS) to visually identify these points.

Step2: Use the graphing calculator

Input the function \(h(x)=x^{4}-3x^{3}-2x^{2}+4x + 5\) into the ALEKS graphing calculator. Look for the peaks of the graph. These peaks represent the local maximum points.

Step3: Round the coordinates

After identifying the local - maximum point(s) on the graph, round the \(x\) and \(y = h(x)\) coordinates to the nearest hundredth. In this case, the local - maximum point is found to be \((x,h(x))=(0.47,5.92)\).

Answer:

\((x,h(x))=(0.47,5.92)\)