Q

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

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

(iii) $h(x) = x^3 + x^2 + x +1$

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Given function is
$h(x) = x^3 + x^2 + x +1$
$h^{'}(x) = 3x^2+2x+1\\ h^{'}(x) = 0\\ 3x^2+2x+1 = 0\\ 2x^2+x^2+2x+1 = 0\\ 2x^2 + (x+1)^2 = 0\\$
But, it is clear that there is no $c \ \epsilon \ R$ such that $f^{'}(c) = 0$
Hence, the function $h(x) = x^3 + x^2 + x +1$ does not have  either maxima or minima

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