Question

How do you graph y=-x^3-x^2+5x?

Answer 1

`y=f(x)=-x^3-x^2+5x`

This is a cubic function with a negative `a` value, so its end behavior is:
`lim_(x->-oo)f(x)=oo`
`lim_(x->oo)f(x)=-oo`

`y=-(x)(x^2+x-5)`
From the factored form above, there is a zero at `x=0`, so `f(0)=0`

`f(x)=-x^3-x^2+5x`

`f'(x)=-3x^2-2x+5=-(x-1)(3x+5)`
`f'(x)` changes sign at `x=-5/3` and at `x=1`. It changes from negative to positive at x=-5/3 and from positive to negative at x=1. This shows how the slope of `f(x)` changes.