### Home > APCALC > Chapter 10 > Lesson 10.2.1 > Problem10-114

10-114.

For the function defined below, determine the values of $a$ and $b$ such that $f$ is both continuous and differentiable for all values of $x$. Justify your answer. Homework Help ✎ $f ( x ) = \left\{ \begin{array} { l l } { a x ^ { 2 } } & { \text { for } x \leq 1 } \\ { b x + 2 } & { \text { for } x > 1 } \end{array} \right.$

$\text{continuous: }a(1)^2=b(1)+2$

$\text{differentiable: }2a(1)=b$