Apentix/AP Calculus AB/Unit 5: Analytical Applications of Differentiation/Question
AP Calculus ABeasymcq1 pt

The Mean Value Theorem applied to f(x)=x2f(x)=x^2 on [0,3][0,3] guarantees f′(c)=3f'(c)=3 for some cc in (0,3)(0,3). What is cc?

A.32\dfrac{3}{2}
B.33
C.92\dfrac{9}{2}
D.34\dfrac{3}{4}

Explanation

Core Concept

Set f′(c)=2cf'(c)=2c equal to the average rate (f(3)−f(0))/3=(9−0)/3=3(f(3)-f(0))/3=(9-0)/3=3. Solving 2c=32c=3 gives c=3/2c=3/2.

Correct Answer

A32\dfrac{3}{2}

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