Activity 3.5.3

Find the exact absolute maximum and minimum of each function on the stated interval.

1. $h(x) = xe^{-x}$, $[0,3]$

2. $p(t) = \sin(t) + \cos(t)$, $[-\frac{\pi}{2}, \frac{\pi}{2}]$

3. $q(x) = \frac{x^2}{x-2}$, $[3,7]$

4. $f(x) = 4 - e^{-(x-2)^2}$, $(-\infty, \infty)$

5. $h(x) = xe^{-ax}$, $[0, \frac{2}{a}]$ ($a \gt 0$)

6. $f(x) = b - e^{-(x-a)^2}$, $(-\infty, \infty)$, $a, b \gt 0$