Consider the function f(x)= cases x^ 2 , & x 1, 2x-1, & x>1

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

Problem

Consider the function

f(x)=\begin{cases} x^{2}, & x\le 1,\\ 2x-1, & x>1. \end{cases}

Answer the following: (i) Verify the continuity of

f

x=1

. (ii) Determine whether

f

is differentiable at

x=1

by evaluating the appropriate limits. State your conclusion clearly.