Question:
Show that the function $f$ given by $f(x)=10^{x}$ is increasing for all $x$ ?
Solution:
we have,
$f(x)=10^{x}$
$\therefore f^{\prime}(x)=10^{x} \log 10$
Now,
$X \in R$
$\Rightarrow 10^{x}>0$
$\Rightarrow 10^{x} \log 10>0$
$\Rightarrow f^{\prime}(x)>0$
Hence, $f(x)$ in an increasing function for all $x$