The correct option is B Only one minimum f'(x)=24x^3+10x =x(24x^2+10) f'(x) gt;0 for x gt;0 f'(x) lt;0 for x lt;0 So ...

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Range of Quadratic Expression

fx=4+5x2+6x4 ...

Question

$f (x) = 4 + 5 x^{2} + 6 x^{4}$ has

Only one minimum

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Neither maximum nor minimum

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Only one maximum

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No minimum

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Solution

The correct option is B Only one minimum
$f^{'} (x) = 24 x^{3} + 10 x$
$= x (24 x^{2} + 10)$
$f^{'} (x) > 0$ for $x > 0$
$f^{'} (x) < 0$ for $x < 0$
So $f (x)$ is minimum at $x = 0$

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