For what value(s) of is the function h(x)= cases kx^2,& x 2 8x-k,& x>2 cases…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

For what value(s) of

k

is the function

h(x)=\begin{cases}kx^2,& x\le 2\\ 8x-k,& x>2\end{cases}

differentiable at

x = 2

? (a)

k=2

(b)

k=\dfrac{16}{5}

k

makes

h

differentiable at

x=2

. (d)

k=2 \text{ or } k=\dfrac{16}{5}