Question(1 point) Find the extreme values of the function $f$ on the interval $[0, \pi]$, and the $x$-value(s) at which they occur. If an extreme value does not exist, enter DNE for both the value and location. $$f(x)=3 e^{x} \cos x$$
Absolute minimum value: $\square$ , located at $x=$ $\square$ .
Absolute maximum value: $\square$ , located at $x=$ $\square$

Studdy Solution
Compare the values to find the absolute minimum and maximum:
1. $f(0) = 3$
2. $f\left(\frac{\pi}{4}\right) = \frac{3\sqrt{2}}{2} e^{\frac{\pi}{4}}$
3. $f(\pi) = -3e^\pi$
The absolute minimum value is $-3e^\pi$, located at $x = \pi$.
The absolute maximum value is $\frac{3\sqrt{2}}{2} e^{\frac{\pi}{4}}$, located at $x = \frac{\pi}{4}$.
Absolute minimum value: $-3e^\pi$, located at $x = \pi$.
Absolute maximum value: $\frac{3\sqrt{2}}{2} e^{\frac{\pi}{4}}$, located at $x = \frac{\pi}{4}$.