Let f(x)= cases x^ 2 , & x<1, |x-1|+1, & x 1

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

f(x)= \begin{cases} x^{2}, & x<1,\\ |x-1|+1, & x\ge 1. \end{cases}

Determine whether

f

is differentiable at

x=1

. State the numerical value of each one-sided derivative and indicate whether they are equal.