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Methods2024 NHT Exam 2 Section A · Q16CAS active1 mark

Derivative of a composite function from tables

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The values for two continuous functions, $f$ and $g$ , and their derivatives are given in the tables below.

| | $x = 0$ | $x = 2$ | |---|---|---| | $f(x)$ | | | | | | |

What is the value of $\frac{d}{dx}\big((g \circ f)(x)\big)$ at $x = 0$ ?

1 mark

A

-3

B

-1

C

0

D

1

E

2

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f (x)

2

-1

f'(x)

-1

2

| | $x = 0$ | $x = 2$ | |---|---|---| | $g(x)$ | $1$ | $-1$ | | $g'(x)$ | $0$ | $3$ |

Two tables. For f: at x = 0, f(x) = 2 and f'(x) = -1; at x = 2, f(x) = -1 and f'(x) = 2. For g: at x = 0, g(x) = 1 and g'(x) = 0; at x = 2, g(x) = -1 and g'(x) = 3.