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

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

Problem

Define

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

Find the value of

k

that ensures

f

is both continuous and differentiable at

x=1

.

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