Find the values of x at which the function f(x) = $e ^ { - 2 x }$ + 2x has a possible relative maximum or minimum point.
A) maximum at x = $\frac { 0.69 } { 2 }$
B) There are no relative maximum/minimum points.
C) minimum at x = 0
D) maximum at x = $\frac { \mathrm { e } } { 2 }$
E) none of these

Question

Quizplus · Accepted Answer

To find relative extrema, we set the derivative f'(x) = 0. The derivative is f'(x) = -2e^(-2x) + 2. Setting this to zero gives -2e^(-2x) + 2 = 0, which simplifies to e^(-2x) = 1. Solving for x gives x = 0. Checking the second derivative, f''(x) = 4e^(-2x), which is positive at x = 0, indicating a minimum.

Find the Values of X at Which the Function F(x) e−2xe ^ { - 2 x }e−2x

Find the Values of X at Which the Function F(x) $e ^ { - 2 x }$