Recent Tutoring Session Reviews
"First meeting with student. Today we worked section introducing concept of derivative of a function. Focused on idea that derivative is just rate of change (or slope) of a function at a point. Worked on several HW problems together, emphasizing the concepts and ideas that were most essential. Helped student to understand the process of solving these problems and to get refreshed on basics from past classwork. Checked our answers to the solution guide and was very satisfied with the results we got together."
"The student and I covered the applications of the first derivative, as well as some applications of the second derivative. He worked very well with these subjects, and seemed to have a firm grasp on the concepts involved. We worked together on his online homework practice problems, and was left his homework to work on. He did not seem to struggle with any of the concepts covered today, even though the second derivative section has not yet been covered in his class. By next week, we will know if there is a quiz or test scheduled for the following week, which we will be able to use as a score to note progress."
"Student has an exam on u-substitution with integration tomorrow. We did practice problems from a textbook I own. About 20. Student understands u-substitution but has trouble recognizing some derivatives and integrations. But student is trying hard on remembering them. Overall good session and I believe he is ready for his exam."
"Today, the student and I reviewed relative extrema. An extreme point is any maximum or minimum on a function. These can be found by taking the first derivative of a function and setting it equal to zero. From there, x is solved on the intervals between the points are tested. If we get a positive number, the function is increasing in this interval. If we get a negative number, the function is decreasing on the interval. A max is the point at which the derivative switches from positive to negative. A minimum occurs at the point at which the derivative switches from negative to positive. The second derivative is also used for extrema. The second derivative test depicts concavity and works similarly to the first derivative test."
"Today, the student and I continued reviewing for his final exam. We practiced finding derivatives using the exponential function, the natural log function, the product rule, the quotient rule, and the chain rule. We did several examples of finding derivatives of functions. The student seemed to understand these problems quite well. Then we did a graphing example. I gave him a polynomial, and he found the critical values for the function. Problems included the function increasing or decreasing, local maximum or minimum, possible points of inflection, and concave up or down. He did very well. He also sketched a graph of the polynomial using the information he found. We will meet again tonight to review for his exam."
"The student is preparing to take a calculus summer course, and to prepare, we went over some of the prerequisites. We talked about tangent lines, limits, and continuity. We'll work on some more basic algebraic topics next time."