Show that the function

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 $x$

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