Mathematics

Mathematics

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

at

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.

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