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Evaluate the derivative of the function at the indicated points. f(x) = x + 108/(x^2). A) f prime...

Question:

Evaluate the derivative of the function at the indicated points.

{eq}f(x) = x + \frac{108}{x^2} {/eq}

A) {eq}{f}' (3) {/eq}

B) {eq}{f}' (6) {/eq}

C) {eq}{f}' (12) {/eq}

Derivative:

Using the power rule we will find the derivative of the function and then we will plug-in the x values that is 3,6 and 12 to get the exact value.

Answer and Explanation:

To find the derivative of the function we will use the power rule:

{eq}\frac{\mathrm{d} x^{n}}{\mathrm{d} x}=nx^{n-1} {/eq}

Now after differentiating it we get:

{eq}f'(x)=1-\frac{2(108)}{x^{3}}\\ =1-\frac{216}{x^{3}} {/eq}

Now let us plug-in the value of x as 3:

{eq}f'(3)=1-8\\ =-7\\ f'(6)=1-1\\ =0\\ f'(12)=1-\frac{1}{8}\\ =\frac{7}{8} {/eq}


Learn more about this topic:

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Solving Partial Derivative Equations

from GRE Math: Study Guide & Test Prep

Chapter 14 / Lesson 1
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