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

AP Calculus ABhardmcq1 pt

Let $g(x)=\int_0^x(t-2)\,dt$ . What is the minimum value of $g$ on the interval $[0,5]$ ?

A.

-2

B.

2

C.

0

D.

\frac{5}{2}

Explanation

Core Concept

$g(x)=\frac{x^2}{2}-2x$ with $g'(x)=x-2$ , so $g$ decreases on $[0,2]$ and increases after. The minimum is $g(2)=2-4=-2$ .

Correct Answer

A $-2$

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