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Activity 3.5.3.
Find the
exact absolute maximum and minimum of each function on the stated interval.
(a)
\(h(x) = xe^{-x}\text{,}\) \([0,3]\)
(b)
\(p(t) = \sin(t) + \cos(t)\text{,}\) \([-\frac{\pi}{2}, \frac{\pi}{2}]\)
(c)
\(q(x) = \frac{x^2}{x-2}\text{,}\) \([3,7]\)
(d)
\(f(x) = 4 - e^{-(x-2)^2}\text{,}\) \((-\infty, \infty)\)
(e)
\(h(x) = xe^{-ax}\text{,}\) \([0, \frac{2}{a}]\) (
\(a \gt 0\))
(f)
\(f(x) = b - e^{-(x-a)^2}\text{,}\) \((-\infty, \infty)\text{,}\) \(a, b \gt 0\)
