The global minimum value of $f (x) = x^{4} - x^{2} - 2 x + 6$ is

6

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8

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4

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non existent

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Solution

The correct option is A $4$
$f (x) = x^{4} - x^{2} - 2 x + 6$
$f^{'} (x) = 4 x^{3} - 2 x - 2 = 2 (2 x^{3} - x - 1)$
for maxima or minima of $f (x)$
$f^{'} (x) = 0 = 2 (2 x^{3} - x - 1) = 2 (x - 1) (2 x^{2} + 2 x + 1)$
$\Rightarrow x = 1$
Hence $f_{m a x} = 4$

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