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Point of Inflection

The total num...

Question

The total number of extremum point(s) for $f (x) = x^{3} + x^{2} + x + 1$ is

0.000

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0.0

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0.00

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Solution

Given, $f (x) = x^{3} + x^{2} + x + 1$
$\Rightarrow f^{'} (x) = 3 x^{2} + 2 x + 1$
$D = 4 - 12 = - 8 < 0$
Hence, $f^{'} (x) > 0 \forall x \in R$
So, There is no critical points for given $f (x)$
$\Rightarrow$ There is no possible point of local maxima/minima.

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