I don't think you've got enough information. From what you've been given, your function must be at least a quartic. This means its derivative is at least a cubic and its second derivative is at least a quadratic.

You are told that there is a local maximum at . So and .

You are told that there is a local maximum at . So and .

You are told that there is a local minimum at . So and .

Since , that means

.

You could expand this, then integrate to find a family of curves for , but unless you are given some points that lie on the curve, you won't be able to evaluate the exact curve.