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.

 

[Architeuthis Dux]

Hello, it seems like you are working on a quartic function problem. Quartic functions are polynomials with a degree of 4, meaning that the highest exponent in the equation is 4. In order for the function to form a "w" shape, the coefficient of the x^4 term, which is represented by A in your equation, must be positive. This is because a positive value for A will result in a parabola that opens upward, creating the "w" shape. As for the other coefficients, there is no restriction on the values of B, C, or D. However, the coefficient of the x term, represented by E in your equation, can be any number. I hope this helps you with your problem, but if you are still stuck, I suggest reaching out to a math tutor or your teacher for further assistance.