# Thread: Critical numbers help

1. ## Critical numbers help

We just started doing local and absolute maximum and minimum numbers and on the practice version of our homework one of the problems says:

Find the value C so that F(x)=2x^(3)-3x^(2)+CX+2 has only one critical number.

How do i solve a problem like this?

2. Originally Posted by GomezH2O
We just started doing local and absolute maximum and minimum numbers and on the practice version of our homework one of the problems says:

Find the value C so that F(x)=2x^(3)-3x^(2)+CX+2 has only one critical number.

How do i solve a problem like this?
When you take the derivative you get a quadratic function.

A quadratic function only has one solution (i.e a reapeated real root) when the discriminant is =0.

The discriminant is the $b^2-4ac$ part of the quadratic equation.

This should get you started.

3. Solved it, and the actual homework problem. Thanks alot