Apentix/AP Calculus AB/Unit 2: Differentiation: Definition and Basic Derivative Rules/Question
AP Calculus ABmediummcq1 pt

Which of the following limits is equal to f′(2)f'(2)?

A.lim⁡x→2f(x)\lim\limits_{x\to 2} f(x)
B.lim⁡h→0f(2+h)−f(2)2\lim\limits_{h\to 0}\dfrac{f(2+h)-f(2)}{2}
C.lim⁡h→0f(2+h)+f(2)h\lim\limits_{h\to 0}\dfrac{f(2+h)+f(2)}{h}
D.lim⁡h→0f(2+h)−f(2)h\lim\limits_{h\to 0}\dfrac{f(2+h)-f(2)}{h}

Explanation

Core Concept

This is the limit definition of the derivative, lim⁡h→0f(x+h)−f(x)h\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}, evaluated at x=2x=2. It equals f′(2)f'(2) by definition.

Correct Answer

Dlim⁡h→0f(2+h)−f(2)h\lim\limits_{h\to 0}\dfrac{f(2+h)-f(2)}{h}

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