Question

Is `f(x)=x^2(x-2)-3x` increasing or decreasing at `x=1`?

Answer 1

`f(x)` is decreasing at `x=1`

Explanation:

To check if the function is increasing or decreasing at a certain point we should find the derivative at this point:

Let us find `f'(x)`
`f'(x)=(x^2)'(x-2)+x^2(x-2)'-(3x)'`
`f'(x)=2x(x-2)+x^2(1)-3`
`f'(x)=2x^2-4x+x^2-3`
`f'(x)=3x^2-4x-3`

Let's compute `f'(1)`
`f'(1)=3(1)^2-4(1)-3`
`f'(1)=3-4-3`
`f'(1)=-4`
`f'(1)<0`
Then, `f(x)` is decreasing at `x=1`