The function f(x) = 3x⁵ + Ax⁴ + Bx³ has inflection points at x = 0, x = -1, and x = 1. Find the values of the constants A and B. A) A = 0, B = -10 B) A = 0, B = 10 C) A has any value, B = -10 D) A has any value, B = 10 E) A = 10, B = 0

Question

Quizplus · Accepted Answer

The second derivative of f(x) is f''(x) = 60x³ + 12Ax² + 6Bx. For f(x) to have inflection points at x = 0, x = -1, and x = 1, f''(x) must be zero at these points.f''(0) = 0 + 0 + 0 = 0f''(-1) = -60 + 12A + 6B = 0f''(1) = 60 + 12A + 6B = 0Solving these equations, we get A = 0 and B = -10.

The Function F(x) = 3x5 + Ax4 + Bx3 Has

The Function F(x) = 3x⁵ + Ax⁴ + Bx³ Has