AP Calculus AB – Mean Value Theorem

AP Calculus students tend to find problems involving the Mean Value Theorem very difficult. I often tell my students “If you don’t know what a problem is asking for, try using the Mean Value Theorem.”  This is due to the fact that most problems where the Mean Value Theorem is needed never actually mention the theorem in the problem itself.

Let’s try a very basic AP Calculus AB Mean Value Theorem problem (note that any Calculus AB problem can also appear on the BC exam). I will provide a full explanation for this problem tomorrow. In the meantime, feel free to leave your own solutions in the comments.

Level 2 Mean Value Theorem Problem

Let f(x) = –3x² + x – 5. A value of c that satisfies the conclusion of the Mean Value Theorem for f on the interval [–2,2] is

(A) –2
(B) –1/2
(C) –1/6
(D) 0

More AP Calculus Problems with Explanations

If you are preparing for one of the AP Calculus exams, you may want to take a look at one of the following books.

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