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Question
Prove that the following function do not have maxima or minima:
f(x) = ex
Solution
Given function, f‘(x) = ex
∴ f‘(x) = ex
= f' (x) = ex ∀ x ∈ R
f' (x) = ex > 0 ∀ x ∈ R
f has no critical point.
Thus, there is no point at which f can have an extremum.
∴ f has neither a maximum nor a minimum.
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