Math 1500 Distance: Tips for Assignment 4

Published: Tue, 02/26/13


 
Did you read my tips on how to do well in Math 1500 Distance.  If not, here is a link to those important suggestions:
How to do Well in Math 1500 Distance 
 
Tips for Assignment 4
Even if you are not taking the distance course, I think it is very useful for all Math 1500 students to attempt these hand-in assignments.  In general, the assignments can be quite demanding and really force you to solidify your math skills.  
 
Here is a link where you can download a copy of Assignment 4:
Math 1500 Distance Assignment 4 (Jan 2013) 
 
You should thoroughly study Lesson 9: Curve-Sketching before attempting this lesson.
 
Be sure to compute and simplify the necessary derivatives and double-check you are right before you proceed to answer the questions.
 
Question 1 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 (i.e. make a table of values for each).  Recall, as I say in Lesson 9, eu has no zeros.
 
Question 2.  Similar to question 5 in my Lesson 9.

Question 3 is a Mean Value Theorem question.  Click the link below for the procedure to follow to "verify" the Mean Value Theorem:
The Mean Value Theorem
 
Question 4.  This question is pretty challenging.  Some hints: Pull all the terms over to the left side of the inequality so that you instead are trying to prove that cosx + x - 1 is greater than or equal to 0.  Let f(x) = cosx + x - 1.  Apply the Mean Value Theorem to that function like you did in question 3 above.  Use [0, x] for your interval [a, b].
 
Question 5.  Consider the conditions f(x) must meet in order for Mean Value Theorem to apply.  Is the function continuous on [a, b]?  Is it differentiable on (a, b)?  Which is to say, is the derivative defined for all values between a and b?  Look for bottom zeros.  A function or derivative is undefined if the bottom is zero.  If the function is not continuous, or not differentiable, then the Mean Value Theorem does not apply, and so it is no surprise if the Mean Value Theorem does not work.
 
Question 6 is analyzing f ' (x).  The first derivative tells you where a function is increasing or decreasing and if the critical points are local maximums or minimums.  Be sure to give the (x, y) coordinates of all the local extremes you identify.
 
Question 7 is 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.
 
Question 8 is a classic curve-sketch.  Just like my questions 3 and 4 in the Lecture.  This is the question you must be able to do on your final exam.