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AP® Calculus AB-BC

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Difficult

Using Second Fundamental Theorem to Find Maximum

APCALC-1GS7QR

Functions $g(x)$ and $f(x)$ are defined as:

$f(x)=x^{2}+3x-18$
$g(x)=\int _{-10 }^{ x }{ f(t)dt } $

At what position $x$ does $g(x)$ have a maximum?

A

$x=3$

B

$x=-6$

C

$x=-6$ and $x=3$

D

$x=-\cfrac{3}{2}$