Question

Find a cubic function f(x) = ax^3 + bx^2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 at x = 1.

Answer 1

i am having trouble at the stage where you combine the functions together to solve for a or b

Answer 2

you know a couple things

Answer 3

you know \(f(-3)=3\) and \(f(1)=0\)

Answer 4

you also know
\[f'(x)=3ax^2+2bx+c\] and \(f'(-3)=0, f'(1)=0\)