For the function {eq}f(x) = 3x^{4} - 2x^{3} - 3x^{2} + 7 {/eq}, find {eq}f''(x) {/eq}. Then find {eq}f''(0) {/eq} and {eq}f''(2) {/eq}.

Question:

For the function {eq}f(x) = 3x^{4} - 2x^{3} - 3x^{2} + 7 {/eq}, find {eq}f''(x) {/eq}. Then find {eq}f''(0) {/eq} and {eq}f''(2) {/eq}.

Power Rule:

The power rule is one of the most commonly applied differentiation rules. It is what we use whenever we differentiate a polynomial, as we will be doing here. Recall that the power rule is

{eq}\begin{align*} \frac{d}{dx} \ x^n &= nx^{n-1} \end{align*} {/eq}

We will need to apply this twice, then plug a couple values into our general result.

Answer and Explanation: 1

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We have

{eq}\begin{align*} f' (x) &= \frac{d}{dx} \left( 3x^{4} - 2x^{3} - 3x^{2} + 7 \right) \\ &= 12x^3 - 6x^2 - 6x \end{align*} {/eq}

And...

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Power Rule for Derivatives: Examples & Explanation

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Chapter 19 / Lesson 18
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In this lesson, learn the power rule for the derivative of exponents. Moreover, learn to understand how to apply the power rule of derivatives for various cases including negative powers.


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