Question

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

Answer 1

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

The domain is: `(-oo,oo)`.

So:

`y'=1/(ln7(1+x^2))*2x`

The function is increasing in `(0,+oo)`, decreasing in `(-oo,0)` and in `x=0` there is a local minimum.

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