Horizontal tangent/point of inflection problem

[drandhawa]

Homework Statement

The function y=x(to the forth)+bx(squared)+8x+1 has a horizontal tangent and a point of inflection for the same value of x. What must be the value of b?

Homework Equations

I think you have to find the derivative, set it equal to 0 and solve for x

The Attempt at a Solution

 

[Dick]

That's one thing you have to do alright. But the second derivative also has to be zero, doesn't it? I would suggest you solve the equation for the second derivative equal to zero for b and substitute it into the first equation. THEN solve for x.