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For the function {eq}f(x)=2x^4-3x^3-4x^2+4{/eq}, find {eq}f''(x){/eq}. Then find {eq}f''(0){/eq} and {eq}f''(5){/eq}.

Question:

For the function {eq}f(x)=2x^4-3x^3-4x^2+4{/eq}, find {eq}f''(x){/eq}. Then find {eq}f''(0){/eq} and {eq}f''(5){/eq}.

Using the Properties of Derivatives

By definition, the derivative is computed as by finding the limit of a rational function which is equal to the slope of secant line which requires some brute force. Now, we derive some properties of derivatives to simplify the computation of derivatives.

Answer and Explanation: 1

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Using the following property

{eq}\displaystyle \frac{d}{dx}\left( x^n \right) = nx^{n - 1} \quad (1) {/eq}


The first derivative is computed as...

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Derivatives: The Formal Definition

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Chapter 7 / Lesson 5
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The derivative in calculus is the rate of change of a function. In this lesson, explore this definition in greater depth and learn how to write derivatives.


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