A function satisfies and

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

A function

g

satisfies

\lim_{x\to 3^-}\frac{g(x)-g(3)}{x-3}=4

and

\lim_{x\to 3^+}\frac{g(x)-g(3)}{x-3}=-1

. Which statement about

g

x=3

is true? (a)

g

is differentiable at

x=3

with

g'(3)=\frac{3}{2}

. (b)

g

is not differentiable at

x=3

because the one-sided limits are unequal. (c)

g

is differentiable at

x=3

with

g'(3)=-1

. (d)

g

is not continuous at

x=3

because the one-sided limits are unequal.