Functions and are differentiable at and satisfy the following: f(2)=3

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Functions

f

and

g

are differentiable at

x=2

and satisfy the following:

f(2)=3,\qquad f'(2)=-1,\qquad g(2)=-4,\qquad g'(2)=5.

Let

P(x)=f(x)g(x)

. (a) Determine the value of

P'(2)

. (b) Explain, using complete sentences, why knowledge of both

f'(2)

and

g'(2)

is essential for finding

P'(2)

. Your explanation should reference the quantities calculated in part (a).