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

Question

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

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Answer

$f(x)=x^3-a x$
$f^{\prime}(x)=3 x^2-a$
Given: $f(x)$ is increasing on $R$.
$\Rightarrow f^{\prime}(x) \geq 0 \forall x \in R$
$\Rightarrow 3 x^2-a \geq 0 \forall x \in R$
$\Rightarrow a \leq 3 x^2 \forall x \in R$
The least value of $3 x^2$ is $0$ .
$\therefore a \leq 0$

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