AP Calculus AB: 3.3 Differentiating Inverse Functions – Exam Style questions with Answer- MCQ

Question

Let

$f$

and

$g$

be inverse functions that are differentiable for all 

$x$

. If f(3)=−2 and g′(−2)=−4, which of the following statements must be false?

I \(f{}'(0)=\frac{1}{4}\)

II \(f{}'(3)=-\frac{1}{4}\)

III. \(f{}'(5)=-\frac{1}{4}\)

A I only

B II only

C III only

D I and III only