# Thread: Critical Numbers & Extremas

1. ## Critical Numbers & Extremas

Given the equation y=2x^2-8x+9, find the extreme values of the function and where they occur.

I know I have to find the derivative, then the critical numbers, but when it comes time for the number line, am I plugging numbers into the original equation or the derivative??

Alsooo, what happens after that?

2. you are trying to determine the sign of f'(x) for values between critical numbers ...

3. Originally Posted by skeeter
you are trying to determine the sign of f'(x) for values between critical numbers ...
I don't understand.
See, my teacher told me to first find the derivative, then find the critical numbers, and then make a number line with the critical numbers. So you'd have to pick a number on that line, and plug it in to determine whether you have a max value or min value.
The problem is, Idk if I plug the number from the number line into the derivative of the equation, or the original equation.

Did that confuse you?

4. no, but my response obviously confused you.

once again ... where will you "plug" in those numbers if you have to determine the sign of f'(x) between the critical values?

5. ohh.. xD
now i get it.

ok, how would i find what the minimum value is at x=2 ?

6. minimum values occur when f'(x) changes sign from negative to positive ... why?

7. ok, on the left of the two, i get a neg.. at the right of two, i get a pos.
so is the min at x=2? or do i have to plug 2 into the original equation?
because the back of the book says that the min. is at 1.. so idk..

8. $\displaystyle y=2x^2-8x+9$ has a minimum at $\displaystyle x = 2$

the minimum value is $\displaystyle y = 1$

9. ok, but how did you get that the minimum value is at y=1??

10. plug 2 in for x, calculate the value of y.

11. Originally Posted by skeeter
plug 2 in for x, calculate the value of y.

Thank you very much.
You've been a huge help for the both of us.