Prove that the following functions do not have maxima or minima:
$h (x) = x^{3} + x^{2} + x + 1$

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Solution

Given, $h (x) = x^{3} + x^{2} + x + 1$
$h^{^{'}} (x) = 3 x^{2} + 2 x + 1$
Here $h^{'} (x) > 0$ for all real $x$ which means, $h (x)$ is a continuous increasing function and will have no maxima or minima.

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