#### Question

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

#### Solution

\[f\left( x \right) = a^x \]

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

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

\[ \Rightarrow f'\left( x \right) > 0\]

\[ \Rightarrow a^x \log a > 0\]

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

\[ \Rightarrow a > 0\]

\[ \Rightarrow a^x > 0\]

\[\text { We know,} \]

\[ a^x \log a > 0\]

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

\[ \Rightarrow \log a > 0\]

\[ \Rightarrow a > 1\]

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

Is there an error in this question or solution?

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