### Home > APCALC > Chapter 9 > Lesson 9.3.1 > Problem9-84

9-84.

Determine values of $k$ and $m$ such that $f$, given below, is differentiable for all $x$.

$f ( x ) = \left\{ \begin{array} { l l } { k x ^ { 2 } - 3 x + 2 } & { \text { for } x < 2 } \\ { 5 x + m } & { \text { for } x \geq 2 } \end{array} \right.$

$kx^2-3x+2=5x+m\text{ when }x=2$

AND

$\frac{d}{dx}(kx^2-3x+2)=\frac{d}{dx}(5x+m)\text{ when }x=2$