Find {eq}f'(x){/eq} for the following function: {eq}f(x)= -8x+2{/eq}

Then find {eq}f'(3), f'(0){/eq}, and {eq}f'(-1){/eq}.

Question:

Find {eq}f'(x){/eq} for the following function: {eq}f(x)= -8x+2{/eq}

Then find {eq}f'(3), f'(0){/eq}, and {eq}f'(-1){/eq}.

Derivatives

f'(x) is defined as {eq}\displaystyle \frac{d}{dx} f(x) {/eq}.Derivative gives the rate of change of a function with respect to the variable.

{eq}\displaystyle f'(x=x_0) {/eq} gives the value of the derivative at particular value of {eq}\displaystyle x= x_0 {/eq}

Formulae used:

{eq}\displaystyle \frac{d(x^{n})}{dx} = n x^{(n-1)} {/eq}.

Answer and Explanation: 1

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Given

{eq}\displaystyle f(x) = -8x+2 {/eq}

On differentiating

{eq}\displaystyle f'(x) = \frac{d}{dx} (-8x+2) \\ f'(x) = -8 \quad \left[...

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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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