Recent Tutoring Session Reviews
"We went through several optimization and extrema word problems. We practiced setting up equations from the description and writing the function we want to optimize in terms of just one variable. We also looked at using the graphing calculator to graph the function and its derivative and generate a table of values. The student is doing well optimizing a function by setting the derivative to zero and she is getting better generating the functions that we want to optimize."
"We covered taking derivatives using the chain, product, and quotient rules; finding the equation of a line tangent to a function at a given point; using first and second derivatives to determine the intervals on which a function is increasing/decreasing and concave up/down. I left a textbook and solutions manual for extra practice."
"We covered u-substitutions for integration problems, and then we covered a review that she had for class. The student continues to struggle with in-class quizzes, but was able to gain points back on a previous test that she had corrected. She had everything she would need for her upcoming test."
"The student and I spent our session going over mean-value theorem and L'Hopital's rule. We combined brief discussion of the concepts with working through a significant number of problems. He was able to grasp all the concepts very quickly and just needs to practice them until the process becomes natural. The most challenging section we covered was related to L'Hopital's rule in cases where the given functions were not in one of the required indeterminate forms. Figuring out the best method to convert those problems to an appropriate indeterminate form can be very difficult. I recommended that the student focus his practice on that style of problem over the other, more straightforward L'Hopital's problems."
"Today we solved 4 problems that involved minimizing or maximizing a function of one variable. The window with a semicircle top was to have maximal area given the width x and perimeter 32. Here, we had to express height y in terms of perimeter and maximize area. Other problems involved movement of ships in straight lines, and figuring when they are the closest. An interesting case occurred when we minimized time taken for the person to row/run across the river. Turns out that the total time has no local minima, and the person had to row straight to the final point. The student needs to practice more of these examples to get acquainted and comfortable, but he is catching on quickly."
"We covered finding critical points using properties of a derivative, finding intervals of increase/decrease, and classifying critical points. The student's homework gave her two derivative functions where these three properties were found. Mechanically, the problems are not as hard as some of the things we have done, but a strong conceptual foundation is needed to do these problems. The majority of our session dealt with trying to get her up to speed in understanding what a derivative is graphically."