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Final Exam Prep Seminar Scheduled
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I am not ready to take registrations yet, but I want to let you know that the Final Exam Seminar will be Thursday, December 4 from 9:00 am to 6:00 pm, and will be held on the UM campus (room 100 St. Paul's College). I will send you an email when I am ready to
take registrations.
Did you read my tips on how to study and learn Math 1500? If not, here is a link to those important suggestions: These are tips for the 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. Here is a link to the actual assignment, in case you don't have it: Study Lesson 9 (Curve-Sketching) from
my Intro Calculus book to prepare for this assignment.
Don't have my book? You can download a free sample of my book and audio lectures containing Lessons 1 and 2: 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). Recall, as I say in Lesson 9, e^u has no
zeros.
In part (c), you will get a negative exponent when you do the derivative. Pull that down to the denominator and then get a common denominator to properly identify the top and bottom zeros. You may find it easier to just guess at what the top and bottom zeros are. Be organized. Sub in x=0, 1, -1, 2, -2, ... There is no shame in just using trial and error to find zeros when things are difficult to factor. Facts are
facts. If you find an x-value that causes either a top or bottom zero, then there is no doubt. Hint: There are three critical numbers in part (c).
Similar to my Lesson 9, question 5. Make sure you include the sentences I box in in your
answer as that is necessary to justify your conclusions.
This is a Mean Value Theorem question. Click the link below for the procedure to follow to
"verify" the Mean Value Theorem: You are analyzing f ' (x). The first derivative tells you where a function is increasing or decreasing and if the critical points are local maximums, local minimums, or
neither. Be sure to give the (x, y) coordinates of all the local extremes you identify. Make sure you look at the tips on page 276 for assistance in simplifying your derivatives. You may also find my Practise Problem 1 at the end of Lesson 9 (page 287) helpful in checking your derivative for part (a).
You are analyzing f '' (x). The second derivative tells you where a function is concave up or concave down and if you have inflection points. Be sure to give the
(x, y) coordinates of all the inflection points you identify.
A classic curve sketch problem. Expect something similar on your final exam.
Note that, when you have a vertical asymptote, there must be a curve drawn on both the left and right side of the vertical asymptote. If one side lacks any points of
interest, you can plot a "random" point to help orient yourself (just add a relevant x value to your table of values). Alternatively, you can also visualize what the curve in that section must look like by using your first and second derivative sign diagrams to guide you.
Take a look at my Practise Problem 2 for a similar example.
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