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?

Question

Hi, this is a problem from my BC Calculus sample exam. I beleive this is a Calc 1 question.

Answer 1

Given y' = 4x^3 + 2bx + 8 = 0 slope = 0
y'' = 12x^2 + 2b = 0 inflection
2x^3 + bx + 4 = 0
6x^2 + b = 0
b = -6 (x = 1)

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