### Home > CALC > Chapter 7 > Lesson 7.2.4 > Problem7-103

7-103.

Find values for $a$, $b$, $c$, and $d$ so that $f(x)$ below is continuous and differentiable for all values of $x$.
$f ( x ) = \left\{ \begin{array} { c c c } { 2 ^ { x } } & { \text { for } } & { x < 0 } \\ { a x ^ { 2 } + b x + c } & { \text { for } } & { 0 \leq x \leq 4 } \\ { d } & { \text { for } } & { x > 4 } \end{array} \right.$

Continuous implies that the pieces of the function agree at the boundary points.
Differentiable implies that the pieces of the derivative agree at the boundary points.

For each boundary point, $x = 0$ and $x = 4$, write and solve a system of equations.
One equation connects $f(x)$, the other connects $f^\prime(x)$.