Define f(x)= cases x^ 2 ! ( 1 x ),& x<0

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Define

f(x)=\begin{cases}x^{2}\sin\!\left(\dfrac1{x}\right),& x<0,\\ c|x|,& x\ge 0.\end{cases}

For which values of the constant

c

f

continuous at

x=0

but not differentiable there? (a)

c=0

(b) All real

c

c

with

c\ne0

(d) There is no real value of

c

that satisfies the given condition