Question

Function $f\left(x\right)=a^x$ is increasing on $R$ if

• A. $a>0$
• B. $a<0$
• C. $0<a<1$
• D. $a>1$

Answer 1

Answer: (D)

$a>1$

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

$f\left(x\right)$ is an increasing function if $f^{\prime }\left(x\right)$ satisfies on $R$

$f\left(x\right)=a^x⟹f^{\prime }\left(x\right)=a^x\left(\log a\right)$
Now, if $a>1$ $⟹\log a>0⟹a^x\log a>0$

$⟹f^{\prime }\left(x\right)>0$

Thus, $f\left(x\right)$ is increasing if $a>1$.

Hence, option D is correct.