Prove that the function does not have maxima or minima: f(x) = e^… - Vidyadip

Question

Prove that the function does not have maxima or minima: $f(x) = e^x$

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Answer

$f(x) = e^x$
$\Rightarrow f'(x) = e^x$
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 $\in$ R such that f'(c) = 0
Hence, function f does not have maxima or minima.

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