# How do you find the intervals in which f (x) = log_7(1+x^2) is increasing or decreasing?

May 25, 2015

A function is increasing where the derivative is positive and negative when it is negative.

The domain is: $\left(- \infty , \infty\right)$.

So:

$y ' = \frac{1}{\ln 7 \left(1 + {x}^{2}\right)} \cdot 2 x$

The function is increasing in $\left(0 , + \infty\right)$, decreasing in $\left(- \infty , 0\right)$ and in $x = 0$ there is a local minimum.

graph{log(1+x^2)/ln7 [-10, 10, -5, 5]}