QuestionAugust 25, 2025

The polynomial function h is defined by h(x)=3x^4+5x^3-4x^2-5x-2 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. YOUR ANSWER (x,h(x))=(square ,square )

The polynomial function h is defined by h(x)=3x^4+5x^3-4x^2-5x-2 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. YOUR ANSWER (x,h(x))=(square ,square )
The polynomial function h is defined by h(x)=3x^4+5x^3-4x^2-5x-2 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. YOUR ANSWER (x,h(x))=(square ,square )

Solution
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Answer

(x,h(x))=(-1.00,5.00) and (x,h(x))=(0.33,-3.17) Explanation 1. Find the derivative Calculate h'(x) = 12x^3 + 15x^2 - 8x - 5. 2. Set derivative to zero Solve 12x^3 + 15x^2 - 8x - 5 = 0 for critical points. 3. Determine local maxima Use the second derivative test or graphing calculator to identify local maxima among critical points. 4. Calculate function values Evaluate h(x) at identified local maxima points.

Explanation

1. Find the derivative<br /> Calculate $h'(x) = 12x^3 + 15x^2 - 8x - 5$.<br />2. Set derivative to zero<br /> Solve $12x^3 + 15x^2 - 8x - 5 = 0$ for critical points.<br />3. Determine local maxima<br /> Use the second derivative test or graphing calculator to identify local maxima among critical points.<br />4. Calculate function values<br /> Evaluate $h(x)$ at identified local maxima points.
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