Calculus 1 : Differential Functions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #1051 : Differential Functions

Find the derivative at \displaystyle x=3.

\displaystyle 5x^3+4x^2

Possible Answers:

\displaystyle 159

\displaystyle 48

\displaystyle 50

\displaystyle 70

Correct answer:

\displaystyle 159

Explanation:

First, find the derivative using the power rule. 

The power rule states,

\displaystyle \frac{d}{dx}x^n=nx^{n-1}.

Applying the power rule to each term in the function results in the following.

\displaystyle \frac{d}{dx}5x^3=15x^2

\displaystyle \frac{d}{dx}4x^2=8x

Thus, the derivative is \displaystyle 15x^2+8x

Now, substitute 3 for x.

\displaystyle 15(3^2)+8(3)

\displaystyle 135+24=159.

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