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# Solution for What Are the Values of 'A' for Which F(X) = Ax is Increasing on R ? - CBSE (Science) Class 12 - Mathematics

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ConceptIncreasing and Decreasing Functions

#### Question

What are the values of 'a' for which f(x) = ax is increasing on R ?

#### Solution

$f\left( x \right) = a^x$

$f'\left( x \right) = a^x \log a$

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

$\Rightarrow f'\left( x \right) > 0$

$\Rightarrow a^x \log a > 0$

$\text { Logarithmic function is defined for positive values of a } .$

$\Rightarrow a > 0$

$\Rightarrow a^x > 0$

$\text { We know,}$

$a^x \log a > 0$

$\text{ It can be possible when } a^x > 0 \text { and } \log a > 0 \text { or }a^x < 0 \text { and } \log a < 0 .$

$\Rightarrow \log a > 0$

$\Rightarrow a > 1$

$\text { So, }f(x)\text { is increasing when }a> 1 .$

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Solution What Are the Values of 'A' for Which F(X) = Ax is Increasing on R ? Concept: Increasing and Decreasing Functions.
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