A function is defined by

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

f(x)=k x^{r}

, where

k

and

r

are constants. The graph of

f

passes through

(2,8)

, and the derivative satisfies

f'(2)=12

. What is the value of

r

? (a) 2 (b) \dfrac{3}{2} (c) 3 (d) \dfrac{3}{4}

Related theory

Exponential Functions
Differentiation Rules
Rules of differentiation
Derivatives
Limits and Derivatives

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