Find the value(s) of a for which f(x) = x^3 - ax is an increasing… - Vidyadip

Question

Find the value(s) of a for which $f(x) = x^3 - ax$ is an increasing function on R.

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Answer

$f(x) = x^3 − ax$
$f'(x) = 3x^2 − a$
Given: f(x) is increasing on R.
$\Rightarrow\text{f}'(\text{x})\geq0\ \forall\ \text{x}\in\text{R}$
$\Rightarrow3\text{x}^2-\text{a}\geq0\ \forall\ \text{x}\in\text{R}$
$\Rightarrow\text{a}\leq3\text{x}^2\ \forall\ \text{x}\in\text{R}$
The least value of $3x^2$ is $0$.
$\therefore\ \text{a}\leq0$

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