Find the absolute extrema of the given function on the indicated interval. on
A) absolute maxima: , absolute minimum:
B) absolute maximum: , absolute minimum:
C) absolute maximum: , absolute minimum:
D) absolute maximum: , absolute minimum:

Question

Find the absolute extrema of the given function on the indicated interval.  on 
A) absolute maxima: , absolute minimum: 
B) absolute maximum: , absolute minimum: 
C) absolute maximum: , absolute minimum: 
D) absolute maximum: , absolute minimum:

Quizplus · Accepted Answer

Since the function is increasing from $-\infty$ to $1$ and then decreasing from $1$ to $\infty$, the absolute maximum must occur at $x=1$ and the absolute minimum must occur at the endpoints of the interval, which are $x=0$ and $x=2$. Evaluating the function at these three critical points gives us:
$$f(0) = 11e^{0} - 11 = -11$$
$$f(1) = 11e^{1} - 11 = 107.18...$$
$$f(2) = 11e^{2} - 11 = 593.70...$$
Thus, the absolute maximum is $f(1) \approx 107.18$ and the absolute minimum is $f(0) = -11$. The correct choice is (C).

Find the Absolute Extrema of the Given Function on the Indicated