Apentix/AP Calculus AB/Unit 8: Applications of Integration/Question

AP Calculus ABmediummcq1 pt

For $f(x)=3x^2$ on $[0,2]$ , the average value of $f$ is 4. At which value of $c$ in $(0,2)$ does $f(c)$ equal the average value?

A.

\frac{4}{3}

B.

\sqrt{2}

C.

\frac{2\sqrt{3}}{3}

D.

\frac{2}{3}

Explanation

Core Concept

The average value is (1/2)∫₀² 3x² dx = 4. Setting 3c² = 4 gives c = 2√3/3, which lies in (0,2).

Correct Answer

C $\frac{2\sqrt{3}}{3}$

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