I understand in an autonomous ODE a root of the derivative is a root of the function. But I will type the question and explain where I don't understand.

1. Consider the differential equation dy/dx = (y+4)(y-5).

(a) What are the two equilibrium solutions y(x) = c, where c is a constant, that make both sides of the equation zero?

(Question I) Would it be y = -4 and y = 5? (Question II) How would that make both sides of the equation zero?

(b) Draw solution curves, as in class notes, for curves with y(0) = -5, and y(0) = 0, and y(0) = 8.

(Question III) I just don't understand this. The y(x) =c statement from the first question seems like its y= c where c is a root of the derivative with respect to x.

How then can I throw these other constants, -5, 0, and 8 into the mix?