What Coefficients Create a W Shape in a Quartic Function?

[lhf454443]

Quartic function Problem! EMS!

I got stuck on a question that tells me to find the restriction on coefficient on equation y=Ax^4+Bx^3+Cx^2+Dx+E, so that the function can form a "w" shape, and I found that a>0 and e can be any thing, but others I cannot find. SO if anyone PLZ help me

 

[HallsofIvy]

In order to have a "w" shape, the function must have two distinct minima and a maximum- that is, the derivative can be written as a product of three linear terms: a(x- u)(x- v)(x- w) with u, v, w distinct numbers.