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

Question

Prove that the following functions do not have maxima or minima:

(i) f(x) = e^x

Answer 1

(i). We have, 

f (x) = e^x

f ' (x) = e^x

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

Therefore, there does not exist c∴ R such that . f '(c) =0

Hence, function f does not have maxima or minima.