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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?

I know that points of inflection are found from the second derivative and setting that function to zero, however the 'b' value really throws me off :yuck:

Oh btw here are the mc answers.

a) -6 b)-1 c) 1 d) 4 e) 6