# 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.

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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...