Set y' and y'' equal to zero, since a horizontal tangent has slope = 0 and the point of inflection is where second derivative=0 (changes curvature/concavity).
You now have a system of 2 equations. Solve for b and x.
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?
To do this i know that y'(x)=y''(x) because they both equal 0 but i tried that but I don't know how to solve because i don't know x.