`f(x) = 4x^5 - 2x^3 + 5x^2` Find the second derivative of the function.

Textbook Question

Chapter 2, 2.3 - Problem 92 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the first derivative of the function:

`f'(x) = (4x^5-2x^3+5x^2)'`

`f'(x) = (4x^5)'-(2x^3)'+(5x^2)'`

`f'(x) =20x^4 - 6x^2 + 10x`

You need to evaluate the second derivative of the function:

`f''(x) = (20x^4)' - (6x^2)' + (10x)'`

`f''(x) = 80x^3 - 12x + 10`

Hence, evaluating the second derivative of the function yields `f''(x) = 80x^3 - 12x + 10.`

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