(B) function $f(x)$ is strictly increasing if $f'(x) > 0$.Given $f(x) = x^3 - 27x + 5$.Differentiating with respect to $x$,we get $f'(x) = 3x^2 - 27$.

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(B) function $f(x)$ is strictly increasing if $f'(x) > 0$.Given $f(x) = x^3 - 27x + 5$.Differentiating with respect to $x$,we get $f'(x) = 3x^2 - 27$.For the function to be strictly increasing,set $f'(x) > 0$:$3x^2 - 27 > 0$$3(x^2 - 9) > 0$$x^2 - 9 > 0$$x^2 > 9$Taking the square root on both sides,we get $|x| > 3$.Thus,the function is strictly increasing when $|x| > 3$.

Class 12 Mathematics Applications of Derivatives Increasing and Decreasing function

Medium

For what values of $x$ is the function $f(x) = x^3 - 27x + 5$ strictly increasing?

A
$x < -3$
B
$|x| > 3$
C
$x \leq -3$
D
$|x| \geq 3$

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Class 12

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Applications of Derivatives

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Increasing and Decreasing function

Let $f$ be a function defined on $[a, b]$ such that $f^{\prime}(x) > 0$ for all $x \in (a, b)$. Prove that $f$ is an increasing function on $(a, b)$.

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If $f(x) = \sin x - \cos x - ax + b$ is a decreasing function for all $x \in R$,then:

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The function $f(x) = x^x$ is a decreasing function in the interval of . . . . . . . $(x \in R^{+})$

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The function $f(x) = \frac{1}{1 + x^2}$ is decreasing in the interval

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If $f(x) = \frac{x}{\sin x}$ and $g(x) = \frac{x}{\tan x}$,where $0 < x \le 1$,then in this interval:

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For what values of $x$ is the function $f(x) = x^3 - 27x + 5$ strictly increasing?

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