Finding b in a Function with Horizontal Tangent and Point of Inflection

[hamburgler]

I'm doing a calc BC practice exam and I found this question that stumps me to the max:

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

Oh btw here are the mc answers.

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

 

[lurflurf]

under what conditions does the function have a hotizontal tangent
Under what conditions does the function have a point of inflection
once you know that it should be easy to see when both occur
you will also see what b must be