Let for all real numbers .

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

g(x)=|x|

for all real numbers

x

. (a) Compute the limit that represents the derivative of

g

x=0

from the left side. (b) Compute the corresponding limit from the right side. (c) Decide whether

g

is differentiable at

x=0

. Provide a clear justification. (d) Describe the geometric feature of the graph of

y=g(x)

x=0

that supports your analytical conclusion.