Question

What are the intervals on which `f(x)=6-x^2` is increasing and decreasing?

Answer 1

Increasing for `x in (-oo,0)`
Decreasing for `x in (0,oo)`

Explanation:

`f'(x)=-2x`

The first derivative of `f(x)` is positive when `x` is less than 0, and `f'(x)` is negative when `x` is greater than 0, so these intervals represent where `f(x)` is increasing and decreasing, respectively.

Increasing for `x in (-oo,0)`
Decreasing for `x in (0,oo)`