Question

determine all critical points
3x^2-96sqrt(x)

Answer 1

hey buddies am waiting

Answer 2

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?

Answer 3

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

Answer 4

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

Answer 5

yes

Answer 6

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.

Answer 7

ok

Answer 8

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

Answer 9

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?

Answer 10

ok. makes sense

Answer 11

i knw how to find the derivative

Answer 12

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

Answer 13

well the derivative will be y=6x-48

Answer 14

if i say thats equal to zero then x=8

Answer 15

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.

Answer 16

I SHUD B FINE FROM HERE. thanks

Answer 17

Okay, glad I could be some help.