Using the derivative of f(x) given below, determine the critical points of f(x).
-$$f ^ { \prime } ( x ) = ( x + 5 ) ^ { 2 } e ^ { - x }$$
A) -3
B) 5
C) -5
D) -5, -3

Question

Quizplus · Accepted Answer

Critical points occur where the derivative is zero or undefined. The derivative $f'(x) = (x + 5)^2 e^{-x}$ is never undefined because the exponential function $e^{-x}$ is always positive. To find where the derivative is zero, set $(x + 5)^2 e^{-x} = 0$. The exponential part $e^{-x}$ cannot be zero, so we only need to solve $(x + 5)^2 = 0$, which gives $x = -5$.

Using the Derivative of F(x) Given Below, Determine the Critical f′(x)=(x+5)2e−xf ^ { \prime } ( x ) = ( x + 5 ) ^ { 2 } e ^ { - x }f′(x)=(x+5)2e−x

Using the Derivative of F(x) Given Below, Determine the Critical $f ^ { \prime } ( x ) = ( x + 5 ) ^ { 2 } e ^ { - x }$