Math 1500: Tips for Assignment 4

Published: Thu, 06/25/15

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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 assignments 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. 

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.  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 (i.e. make a table of values for each).

Part (b) is tricky!  Recall what I teach you about the absolute value function (see Lesson 2, question 4).  The absolute value of 3t-4 is either 3t-4 or -(3t-4) depending on the value of t.  Find the zero for 3t-4 and make a sign diagram.  Then, compute the derivative of each piece.  Note the derivative is undefined at the zero, because the derivatives of each piece disagree as to what the answer should be.  Because the derivative is undefined, that value is a critical number.  The graph is a V-shaped graph, and any V graph has a critical number at the apex of the V (because that point appears to have 2 different tangent lines: the two arms of the V; that is unacceptable, so there is no derivative at that point and no tangent line).
Question 2
Make sure you read my tips on how to compute and simplify derivatives after question 4 in Lesson 9 (starts on page 276).

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:
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.
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.
Question 6
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.