Question

How do you find the intervals of increasing and decreasing using the first derivative given `y=x^2-4x`?

Answer 1

`y=x^2-4x` is increasing in the interval `(2,oo)` and it is decreasing in the interval `(-oo,2)`.

Explanation:

A function `y=f(x)` is increasing in the interval where `(dy)/(dx)>0` and is decreasing in the interval where `(dy)/(dx)<0`,

Here `y=x^2-4x`

hence `(dy)/(dx)=2x-4`

Now `2x-4>0` means `x>2`, hence `y=x^2-4x` is increasing in the interval `(2,oo)`

and `2x-4<0` means `x<2`, hence `y=x^2-4x` is decreasing in the interval `(-oo,2)`

graph{x^2-4x [-10, 10, -5, 5]}