Math 1500: ICYMI Tips for Assignment 4

Published: Thu, 11/05/15

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Did you read my tips on how to study and learn Math 1500?  If not, here is a link to those important suggestions:
Did you see my tips for Assignment 1? Click here.
Did you see my tips for Assignment 2? Click here.
Did you see my tips for Assignment 3? Click here.
Tips for Assignment 4
These are tips for the first assignment in the Distance/Online Math 1500 course, but I strongly recommend that you do this assignment as homework even if you are taking the classroom lecture section of the course.  These assignments are very good (and challenging) practice.  The first assignment is a great way to build and review key skills that will be helpful for this course.

Here is a link to the actual assignment, in case you don't have it:
You should thoroughly study Lesson 9: Curve-Sketching before attempting this lesson.
Question 1
Make sure you read my tips on how to compute and simplify derivatives after question 4 in Lesson 9 (starts on page 276).

This question is asking for the critical numbers.  That means they want the critical points and singular points.  The top and bottom zeros of the first derivative are the critical numbers (if the bottom zero is a vertical asymptote, it is not a critical number).  Make sure you give both the x and y coordinates of your critical numbers, even though it would be fine to just give the x values in this question.
Question 2
Similar to my Lesson 9, question 5.  Also look at Practise Problems 17-19 for additional examples.  Make sure you include the sentences I box in in your answer as that is necessary to justify your conclusions.
Question 3
This is a Mean Value Theorem question.  Click the link below for the procedure to follow to "verify" the Mean Value Theorem:

Be sure to point out that the given function is a polynomial, and so it is certainly continuous and differentiable, therefore the Mean Value Theorem applies.

Hint: You will need the quadratic formula to help solve this problem.
Question 4
Don't forget to make your x,y table of values in this problem to properly determine the x,y coordinates they request.

Recall the tips I gave you about finding the domain of a function back in Lesson 1, questions 2 and 3.  Make sure you are clear about the domain here!

Otherwise, this is doing a complete first derivative analysis as I teach in Lesson 9.

Part (e)
By "first derivative test," they simply mean, use the sign diagram you made for increase/decrease earlier in the problem to visualize whether the critical points are local mins or max.

Part (f)
I discuss and illustrate the second derivative test in Lesson 9, Practise Problem 20.  Note that you are not asked to do any analysis with the second derivative (such as concavity and inflection points), you are just asked to use the second derivative test to check the critical points.  Obviously, you should reach the same conclusion as you did in the previous part.

Note that x=0 is not a critical number because it is a vertical asymptote, not a singular point (it is not in the domain of the function).
Question 5
A classic curve sketch problem. Make sure you have done my Lesson 9, questions 3 and 4, and Practise Problems 1-16 in order to be thoroughly prepared for this problem.

Since you are asked to show all your work, I suggest that you actually compute the k/0 limits and solve the infinity limits formally, as I teach in Lesson 2, to ensure you are not penalized.