Develop Cubic equation with a few points

[LSCupcake]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I know that d= +1 and that's about it. I am really stuck and needs to know this for my summative on Tuesday. If anyone has an idea what to do, pleasseee help.

 

[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?

 

[LSCupcake]

a local min means that the slope is zero...does that mean that y=0?
I still don't understand what to do...do I use elimation with the 3 equations?

 

[Dick]

a local min means that the slope is zero...does that mean that y=0?
I still don't understand what to do...do I use elimation with the 3 equations?

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)?

 

[LSCupcake]

I can't use f'(x) because we learn that in calculas, that is a derivative right? And I haven't taken calculas yet.

 

[Dick]

I can't use f'(x) because we learn that in calculas, that is a derivative right? And I haven't taken calculas yet.

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.