Question

The function $f\left(x\right)=e^{ax}+e^{-ax},a>0$ is monotonically increasing for

• A. $x=-1$
• B. $x<-1$
• C. $x>-1$
• D. $x>0$

Answer 1

The correct option is D $x>0$

Since, $f\left(x\right)=e^{ax}+e^{-ax}$
$\Rightarrow f^{\prime }\left(x\right)=a(e^{ax}-e^{-ax})$
$f\left(x\right)$ is monotonically increasing, if
$f^{\prime }\left(x\right)>0$
$\Rightarrow e^{ax}-e^{-ax}>0$
$\Rightarrow e^{2ax}>1$
$\Rightarrow x>0$