Home > CALC > Chapter 7 > Lesson 7.4.3 > Problem7-198

7-198.

Find $a$ and $b$ so that $f(x)$ below is continuous and differentiable at $x = 1$.

$f ( x ) = \left\{ \begin{array} { l l } { a e ^ { x } } & { \text { for } x \leq 1 } \\ { \operatorname { ln } x + b } & { \text { for } x > 1 } \end{array} \right.$

Write and solve a system of equations, each evaluated at $x = 1$. The first equation will equate the two pieces of $f(x)$.
The second equation will equate the two pieces of $f^\prime(x)$.