Consider $f (x) = a(1 - e^{-bx})$ for $a>0$ and $b>0$.

Find $f'(x)$: $f'(x) =$
Based on your expression for $f'(x)$, is $f(x)$ increasing or decreasing? (Enter increasing or decreasing.)
(Be sure that you can see why this is true for all values of x.)

Find $f''(x)$: $f''(x) =$
Based on your expression for $f''(x)$, is $f(x)$ concave up or concave down? (Enter up or down.)
(Be sure that you can see why this is true for all values of x.)