Question

Let ƒ(x) be a polynomial of degree 3 such that ƒ(-1) = 10, ƒ(1) = -6, ƒ(x) has a critical point at x = -1 and ƒ'(x) has a critical point at x = 1. Then ƒ(x) has a local minima at x = _______.

Answer 1

f''(x) = λ(x - 1)

f'(x) = λx²/2 - λx + c

⇒ f'(-1) = 0 ⇒ c = -3λ/2

Which has minima at x = 3

Answer 2

f(x) = ax³ + bx² + cx + d