Using the derivative of f(x) given below, determine the critical points of f(x).
-$$f ^ { \prime } ( x ) = ( x + 4 ) ^ { 2 } e ^ { - x }$$
A) -4, -2
B) -2
C) -4
D) 4

Question

Quizplus · Accepted Answer

Critical points occur where the derivative is zero or undefined. The derivative $f'(x) = (x + 4)^2 e^{-x}$ is never undefined because the exponential function $e^{-x}$ is always positive. Setting the derivative equal to zero, we find that $(x + 4)^2 = 0$ when $x = -4$, making -4 the only critical point.

Using the Derivative of F(x) Given Below, Determine the Critical f′(x)=(x+4)2e−xf ^ { \prime } ( x ) = ( x + 4 ) ^ { 2 } e ^ { - x }f′(x)=(x+4)2e−x

Using the Derivative of F(x) Given Below, Determine the Critical $f ^ { \prime } ( x ) = ( x + 4 ) ^ { 2 } e ^ { - x }$