A function is continuous for all real numbers and differentiable everywhere except at

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A function

m

is continuous for all real numbers and differentiable everywhere except at

x=1

, where

m'

is undefined. The derivative satisfies

m'(x)=3

for

x<1

and

m'(x)=-2

for

x>1

. Determine whether

m

attains a relative extremum at

x=1

, and state whether the graph of

m

has a sharp corner there.