A twice-differentiable function satisfies and

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

A twice-differentiable function

p

satisfies

p(3)=10

and

p'(3)=4

. A linear approximation at

x=3

is used to estimate

p(3.05)

and yields

10.20

, while the actual value is

10.23

. Determine the sign of

p''(3)

and state whether

p''(3)

is positive, negative, or zero.