Source: Extra Practice
The function f(x) = e^x has:
Options
Option A
One local maximum
Option B
One local minimum
Option C is correct
No local maxima or minima
Option D
Infinite critical points
Explanation
To find local extrema, we look for f'(x) = 0. For f(x) = e^x, f'(x) = e^x. However, e^x is always greater than 0 for all real values of x and never equals zero. Since there are no critical points where the derivative is zero or undefined, the function has no local maxima or minima.