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Q.

Function f(x) = $x^{3} - 27 x + 5$ is monotonically increasing when

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a

x > 3

b

$|x| > 3$

c

x < –3

d

$x \leq - 3$

answer is D.

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Detailed Solution

$f (x) = x^{3} - 27 x + 5 f^{'} (x) = 3 x^{2} - 27$

Function is monotonically increasing

$\Rightarrow f^{'} (x) \geq 0 3 x^{2} - 27 \geq 0 x^{2} - 9 \geq 0$

Question Image

$x \leq - 3, x \geq 3$

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Function f(x) = x3–27x + 5 is monotonically increasing when