Let be defined by for and for

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let

g

be defined by

g(x)=5

for

x<2

and

g(x)=3

for

x\geq2

. Let

G

be an antiderivative of

g

with

G(2)=4

. Describe the continuity and differentiability of

G

x=2

, and give a brief reason for each conclusion.

Related theory

Antiderivatives
Derivative Foundations
Differentiability
Differentiability of functions
Continuity and Differentiability

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