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

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

Problem

Let

f(x)=\begin{cases}x^2, & x<1,\\kx^2-(k-1), & x\geq1.\end{cases}

f

is differentiable at

x=1

, what is the value of

k

? (a)

k=0

(b)

k=1

(c)

k=\dfrac{1}{2}

(d) No such value of

k

exists