Using a calculator or computer, estimate the absolute extrema of on the interval . Round answer to the nearest hundredth.
A) absolute max: ; absolute min:
B) absolute max: ; absolute min:
C) absolute max: ; absolute min:
D) absolute max: ; absolute min:

Question

Using a calculator or computer, estimate the absolute extrema of  on the interval  . Round answer to the nearest hundredth.
A) absolute max: ; absolute min: 
B) absolute max: ; absolute min: 
C) absolute max: ; absolute min: 
D) absolute max: ; absolute min:

Quizplus · Accepted Answer

To find the absolute extrema of the function, we can take the derivative and set it equal to 0 to find critical points. However, since the function is of the form $a^x$ where $a$ is a positive constant, its only critical point is at the boundary of the interval. Thus, we need to evaluate the function at both endpoints of the interval to find the absolute max and min. Plugging in $x=-3$ and $x=4$ gives $11e^{-9}$ and $11e^{16}$, respectively. Therefore, the absolute max is $11e^{16}$ and the absolute min is $11e^{-9}$. Rounding to the nearest hundredth yields $1.16 	imes 10^{14}$ and $0.00$, respectively. Thus, the only choice that is closest to these values is D.

Using a Calculator or Computer, Estimate the Absolute Extrema of