# Homework Help: Develop Cubic equation with a few points

1. Jan 16, 2010

### LSCupcake

1. The problem statement, all variables and given/known data

Write the equation of the cubic function with a y-intercept at 1, a local minimum of (3,1) and through point (2,5)

2. Relevant equations

3. The attempt at a solution
I know that d= +1 and thats about it. Im really stuck and needs to know this for my summative on Tuesday. If anyone has an idea what to do, pleasseee help.

2. Jan 16, 2010

### Dick

Ok, yes d=1. That's a start. So f(x)=a*x^3+b*x^2+c*x+1. You need to find a,b and c. You know f(3)=1 and f(2)=5, right? That's 2 equations in the 3 unknowns a, b and c. You need one more. What does having a local min at x=3 tell you?

3. Jan 16, 2010

### LSCupcake

a local min means that the slope is zero...does that mean that y=0?
I still dont understand what to do...do I use elimation with the 3 equations?

4. Jan 16, 2010

### Dick

Yes, you are going to use elimination with the 3 equations once you get them. A local min means slope is zero, alright, but that doesn't mean y=0, it means f'(3)=0. What's f'(x)?

5. Jan 16, 2010

### LSCupcake

I cant use f'(x) because we learn that in calculas, that is a derivative right? And I havent taken calculas yet.

6. Jan 16, 2010

### Dick

Yes, that's a derivative. If you can't use that then you must have been told something about minima of cubics that will let you get the third equation.