Determine the value of such that the piecewise function k(x)= cases (x-5)^ 2 , & x 5

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

Problem

Determine the value of

a

such that the piecewise function

k(x)= \begin{cases} (x-5)^{2}, & x\le 5,\\ a(x-5)+25, & x>5 \end{cases}

is differentiable at

x=5