Let f(x) = ax^3 + bx^2 +cx+d. Determine the values of a, b, c, and d so that f(x) critical
points at x=2 and x=-1, F(0) = 1, and F'(0) = 6.

has derivative

We want this to have critical points at and ; we want to be 0 or undefined at these points. Since is a polynomial, it is continuous, so the derivative will always exist.

So we need

We also want and . This means

so the previous system reduces to

So the function is

first one

step-by-step explanation: