f(x) = x4-4x3-8x2+4
How many times does f(x) = 0? (excuse the bad formulation)
Hint: Gather as much information from the derivative of f(x) as possible. We are only interested in the number of times f(x) equals zero.
Okay so differentiating the function is simple: f ' (x) = 4x3-12x2-16x, but what kind of information do I need to extract in order to determine how many times f(x)=0?