Question is...
the graph of y=2x^3 - ax^2 - bx + 5 has critical points x=2 and x=-1
find a and b
find and identify all local extremities
Critical points occur at values of x such that $\displaystyle \frac{dy}{dx} = 0$. Therefore $\displaystyle (x - 2)$ and $\displaystyle (x + 1)$ are factors of $\displaystyle \frac{dy}{dx} \, ....$
You now have two expresions for dy/dx. Compare then and hence get the value of a and b.
Forget this. I have a better idea for you.
The two solutions to dy/dx = 0 are x = 2 and x = -1. Substitute these values of x to get two equation with a and b in them. Solve the resulting equations simultaneously.