## anonymous 5 years ago determine all critical points 3x^2-96sqrt(x)

1. anonymous

hey buddies am waiting

2. anonymous

This early in the morning there may not always be someone who can answer a Caclulus question so it may take some time to get an answer. That said, I can help. So, because I won't work the problem for you, let's see if we can figure it out. Do you recall what critical points are?

3. anonymous

yes i do . i know i have to find the max n min values

4. anonymous

Okay, so in general what makes a point a critical point? In other words, how are they defined?

5. anonymous

yes

6. anonymous

So, tell me. How are critical points defined? Understanding that is key to working this problem and we need the definition to proceed to the next step. I'm sorry, but I'm not going to just work the problem for you. I want you to understand how to work these problems in general so you can do them again during, say, an exam.

7. anonymous

ok

8. anonymous

they are thos points in a fuction that the behaviour changes. For instance change in inflection, or moving from max to min or viceversa

9. anonymous

Well, yes and no. Places where a function changes concavity (infection points) are not always critical points. Minimum and maximum points are critical points, but there are also critical points that are not minimum and maximums. So, think of it instead in terms of the function itself. For a general function, say f(x), critical points are defined to be the values of x for which the derivative, f ' (x) is zero or does not exist. So, we need the derivative of your function to find the critical points. What is the derivative of your function?

10. anonymous

ok. makes sense

11. anonymous

i knw how to find the derivative

12. anonymous

Good, so what is the derivative? Or can you do the problem from here?

13. anonymous

well the derivative will be y=6x-48

14. anonymous

if i say thats equal to zero then x=8

15. anonymous

Yes, except your derivative of the second term isn't quite correct. Isn't the derivative of $$\sqrt{x}$$, $\frac{1}{2}x^{-\frac{1}{2}}$ ? That will change your deriviatve and your critical points.

16. anonymous

I SHUD B FINE FROM HERE. thanks

17. anonymous

Okay, glad I could be some help.