# Critical numbers help

• Oct 23rd 2009, 11:44 AM
GomezH2O
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?
• Oct 23rd 2009, 12:17 PM
TheEmptySet
Quote:

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.
• Oct 23rd 2009, 12:22 PM
GomezH2O
Solved it, and the actual homework problem. Thanks alot