Question

If f(x) = x^4+bx^2+8x+1 has a horizontal tangent and a point of inflection for the same value of x, what does b have to be? PLEASE HELP~?

Answer 1

At first, you should use second derivative test to find inflection point(s). Then check, where the tangent of given function is horizontal line. http://mathworld.wolfram.com/InflectionPoint.html

Answer 2

Refer to the attached solution using Mathematica 9 Home Edition.
An earlier answer posting may not have had line numbers attached.