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

AP Calculus ABmediummcq1 pt

Let $g(x)=\int_1^x(t^2-4t)\,dt$ . At which value of $x$ does $g$ have a local minimum?

A.

x=0

B.

x=4

C.

x=2

D.

x=-2

Explanation

Core Concept

By the Fundamental Theorem, $g'(x)=x^2-4x=x(x-4)$ . Since $g'$ changes from negative to positive at $x=4$ , $g$ has a local minimum there.

Correct Answer

B $x=4$

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