Prove that the following functions do not have maxima or minima: f (x) = e x

Question

Philoid · Accepted Answer

f (x) = e^x

⇒ f’(x) = e^x

Now, if f’(x) = 0, then e^x = 0.

But, the exponential function can never assume 0 for any value of x.

Therefore, there does not exist c ϵ R such that f’(c) = 0

Hence, function f does not have maxima or minima.

Prove that the following functions do not have maxima or minima:f (x) = ex