Question

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

Answer 1

Given:
f(-2) = -8a + 4b - 2c + d = 2
f(1) = a + b + c + d = 0

Find the first derivative:
f'(x) = 3ax^2 + 2bx + c

Know critical points:
f'(-2) = 12a - 4b + c = 0
f'(1) = 3a +2b + c = 0

So you have the system of equations:
-8a + 4b - 2c + d = 2
a + b + c + d = 0
12a - 4b + c = 0
3a +2b + c = 0

Answer 2

how do i find a, b, c, d?