Find the value(s) of a for which f(x) = x3 - ax is an increasing … - Vidyadip

Question

Find the value(s) of a for which f(x) = x³ - ax is an increasing function on R.

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Answer

f(x) = x³ − ax
f'(x) = 3x² − 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 3x² is 0.
$\therefore\ \text{a}\leq0$

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