Second Derivative Test

[CoreyyV]

Using the second derivative test, find whether the function: x^3-9x^2-48x+52, when x=8

 

[tkhunny]

Okay, what's stopping you from finding the first two derivatives?

What is the "second derivative test"?

We need to see where you are and what you have tried.

 

[Steven G]

It seems that your question is incomplete.

Using the second derivative test, find whether the function: x^3-9x^2-48x+52 is what, when x=8

 

[CoreyyV]

Okay, what's stopping you from finding the first two derivatives?

What is the "second derivative test"?

We need to see where you are and what you have tried.

I realized that I did not add in the second part of the question which asks to find whether the function has a local minimum or maximum when x=8 using the second derivative test.

I found (what I thought) is the second derivative:
6x-18
Then when x=8, I plugged that into the function and got:
48-18---> 30
I see that it is greater than 0 so I assume that the function has a local minimum, but was unsure if I was correct.

 

[CoreyyV]

It seems that your question is incomplete.

Using the second derivative test, find whether the function: x^3-9x^2-48x+52 is what, when x=8

I'm sorry, I did leave out the second part of the question without realizing it.
The second part is to find whether the function as a local minimum or maximum when x=8 using the second derivative test.

 

[pka]

Using the second derivative test, find whether the function: x^3-9x^2-48x+52, when x=8

Please, Please, read your post. Does it contain a complete question?
If \(y=x^3-9x^2-48x+52\) then \(y"=6x-18\). From that one may ask "where is a point of inflection?"
OR "is the graph of \(y\) concave up at \(x=8~?\)
So what is this question?

 

[CoreyyV]

I mistakenly did not put the complete question in my initial post. The complete question is as followed:

The functionf(x) =x^3−9x^2−48x+ 52 has either a local minimum or local maximum at x= 8. Use the second derivative test to figure out which it is.

 

[CoreyyV]

Please, Please, read your post. Does it contain a complete question?
If \(y=x^3-9x^2-48x+52\) then \(y"=6x-18\). From that one may ask "where is a point of inflection?"
OR "is the graph of \(y\) concave up at \(x=3~?\)
So what is this question?

My apologies for not putting the complete question in my post, it was a mistake. The complete question is as follows:

The function f(x) =x^3−9x^2−48x+ 52 has either a local minimum or local maximum at x= 8. Use the second derivative test to figure out which it is.