Find the absolute extreme values of the function on the interval.
-$$f ( x ) = - 4 e ^ { - x ^ { 2 } } , - \infty

Question

Find the absolute extreme values of the function on the interval.
-$$f ( x ) = - 4 e ^ { - x ^ { 2 } } , - \infty < x < \infty$$
A) Minimum value is $- 4$ at $x = 0$; no maximum value
B) Maximum value is $- 4$ at $x = 0$; minimum value
C) No minimum value and no maximum value
D) Minimum value is $- 4$ at $x = 0$; maximum value is $- \frac { 4 } { \mathrm { e } }$ at $x = 1$

Quizplus · Accepted Answer

The function $f(x) = -4e^{-x^2}$ reaches its highest value at $x = 0$, where it equals $-4$, because the exponential function decreases as $x^2$ increases. There is no maximum value since the function approaches 0 but never reaches it for large values of $x$.

Find the Absolute Extreme Values of the Function on the Interval