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# Solution for Find the Value(S) of a for Which F(X) = X3 − Ax is an Increasing Function on R ? - CBSE (Science) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

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

#### Solution

$f\left( x \right) = x^3 - ax$

$f'\left( x \right) = 3 x^2 - a$

$\text { Given }:f\left( x \right)\text { is increasing on R }.$

$\Rightarrow f'\left( x \right) \geq 0 \forall x \in R$

$\Rightarrow 3 x^2 - a \geq 0 \forall x \in R$

$\Rightarrow a \leq 3 x^2 \forall x \in R$

$\text { The least value of } 3 x^2 \text { is } 0.$

$\therefore a \leq 0$

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Solution Find the Value(S) of a for Which F(X) = X3 − Ax is an Increasing Function on R ? Concept: Increasing and Decreasing Functions.
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