Show that the function f given by f(x)=10^x is increasing for all… - Vidyadip

Question

Show that the function f given by $\text{f}(\text{x})=10^\text{x}$ is increasing for all x.

✓

Answer

We have,
$\text{f}(\text{x})=10^\text{x}$
$\therefore\ \text{f}'(\text{x})=10^{\text{x}}\times\log10$
Now,
$\text{x}\in\text{R}$
$\Rightarrow10^\text{x}>0$
$\Rightarrow10^\text{x}\log10>0$
$\Rightarrow\text{f}'(\text{x})>0$
Hence, f(x) in an increasing function for all x.

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