Show that the function `f` given by `f(x)=10^x` is increasing for all `xdot`

Explanation

Given: `f(x)=10^x`

To show: `f(x)` is increasing for all `x`

Solution: `f(x)=10^x`

`f^prime(x)=10^x log _e 10 quad[therefore log_e10= 1]`

`=10^x>0`

`[therefore log _e 10=1]`

`f^prime(x)>0` for all `x .`

`therefore f(x)` is increasing on all the values of `x`.