Question

The function y=x^4+bx^2+8x+1 has a horizontal tangent and a point of inflection for the same value of x. What must be the value of b? ...?

Answer 1

so f ' (x) = 0 and f ' ' (x) = 0 for the same x . so f '(x) = f '' (x) f ' = 4x^3 + 2bx + 8 = f '' (x) = 12x^2 + 2b