Increasing/Decreasing Concavity

[progamer3054]

I'm having an extremely difficult time doing this. Can anyone offer some assistance? A link to the image of the problem as well as attachments are provided.

The graph of f(x) = (x^2)/(x^3+1) is shown below on the interval (-1, infinity)
1. Use the derivative to find any critical points. Create a sign chart (show your computations) to indicate where this function is increasing and decreasing, and classify each critical point as a local maximum or minimum. Mark these points on the graph, and draw the tangent lines


2. Refer to the function on page 1:
a) Compute the second derivative of f(x)
b) Use a calculator or software to solve for the critical points
c) Create a sign chart (show your computations) to indicate where this function is concave up or concave down, and determine whether the function has a maximum slope or minimum slope at that inflection point
d) Mark the inflection points on the graph, and draw the tangent lines
e) What are the slopes of the tangent lines at the inflection points?

 

[Quaid]

Hi ProGamer:

Are you allowed to ask for help with this quiz question?

If so, have you done any work, yet? That is, have you calculated any derivatives?

Please show what you've done so far.

Here is a link to the summary page of the forum guidelines. (Links to the complete guidelines, and forum rules, appear on that page.)

Cheers

 

[progamer3054]

Hi ProGamer:

Are you allowed to ask for help with this quiz question?

If so, have you done any work, yet? That is, have you calculated any derivatives?

Please show what you've done so far.

Here is a link to the summary page of the forum guidelines. (Links to the complete guidelines, and forum rules, appear on that page.)

Cheers

1. Yes.
2. I have not done any work. I am an entrepreneur and my university felt that I needed to take this calc class despite my not having taken math in a few years. All I need to do is pass this class so I can get this course out of my way so I can never use it again.

Any help you can give regarding the problem would be greatly appreciated.

 

[Quaid]

I have not done any work.

[have not done] math in a few years

All I need to do is pass this class so I can get this course out of my way so I can never use it again.

Hi. I'm not sure that I understand. Are you saying that you want to pass the course without learning the material? If so, you're at the wrong website for help.

Otherwise, we can help you to understand the material, but, if you're in way over your head due to forgetting the prerequisite material for calculus, then I think that a face-to-face tutor would be much better for you -- versus trying to get a lot of intensive tutoring over the Internet.

Your choice, though.

Can anyone offer some assistance?

The graph of f(x) = (x^2)/(x^3+1) is shown below on the interval (-1, infinity)

1. Use the derivative to find any critical points.

The graph does not show the interval (-1, infinity)

The graph shows the interval (-1, 3.5)

I prefer using the Product Rule, for calculating the derivative of a Rational function like yours, instead of using the Quotient rule, because it's generally easier to simplify the result.

This requires first rewriting the function as a product.

f(x) = (x^2)*(x^3+1)^(-1)

Do you remember the Product rule?

Also, (x^3+1)^(-1) is a composite function, so the Chain rule is required for differentiating that part.

Can you use x^2 and (x^3+1)^(-1) and the derivative of each to write out the Product rule. Don't worry about simplifying the result, yet.

If none of this sounds familiar, then my suggestion is to drop this calculus course and tell your adviser that you need a math placement test. Maybe your school did not realize that you have not done any math for years, when they registered you for calculus.

Cheers :cool: