Differentiation of Composite & Inverse Functions (College Board AP® Calculus AB)

Exam Questions

17 mins11 questions

2 marks

$x$	2	3	5	8
$f (x)$	-5	0	7	1
$f^{'} (x)$	-2	3	-4	8
$g (x)$	-6	2	-7	-1
$g^{'} (x)$	4	5	6	-8

The functions $f$ and $g$ are differentiable. The table shown gives the values of the functions and their first derivatives at selected values of $x$ .

Let $h$ be a differentiable function such that $h (x) = f (g (x))$ .

Find the value of $h' (3)$ .

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31 mark

$x$	2	3	5	8
$f (x)$	6	0	7	5
$f' (x)$	2	3	-4	9

The function $f$ is a one-to-one, differentiable function. The table shown gives the values of the function and its first derivatives at selected values of $x$ .

Let $g$ be a differentiable function such that $g (x) = f^{- 1} (x)$ .

Find the value of $g^{'} (5)$ .

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