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AP® Calculus AB-BC

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Difficult

Reverse Engineer Original Function, Given Point and Derivative

APCALC-ZZNEEE

Let $f$ and $g$ be differentiable functions with the following properties:

I. $ g(x) \gt 0$ for all $x$

II. $f(0)=1$

If $h(x)=f(x)g(x)$ and $h'(x)=f(x)g'(x)$, then $f(x)=$

A

$0$

B

$g(x)$

C

$e^x$

D

$1$