Award-Winning Test Prep & Academic Tutoring in North Park, UT

"We first discussed how to graph f'(x) when given a graph of f(x). This can be a bit tricky at first. I first demonstrated how to identify points on f(x) that have a derivative of 0, or horizontal tangent lines. Between any 0-derivative points, we approximated the value of tangent line slope and graphed those values. This allowed us to roughly graph f'(x) on the same set of axes as f(x). This process took a few examples for the student to start picking it up. I told the student that we would spend more time on this concept again at our next session. We again did some review problems that covered derivatives. They progressed in difficulty before I gave her a very complex problem that incorporated power rule, chain rule, product rule, and quotient rule, trig functions, e^x, and ln(x) all into one. It was meant to be intimidating, but we talked through how to break it down into smaller components and solve each one. We also talked about how to find the derivatives of rarer trig functions, such as sec, csc, cot(x), when you can't memorize them. We were able to finally reach the correct derivative solution to this extremely complex question. Afterward, the student breathed a sigh of relief and I congratulated her on solving something more complex than she'll likely see on her exam. I then covered some new topics with the student that introduced some applications of derivatives. This included finding extrema values, the extrema value theorem, concavity, and inflection points. We did one or two examples that required the student to find extreme values, the concavity, and any inflection points within a given range. We then used the last 15-20 minutes of our session to get a head start on the next homework assignment due later in the week."

"Today we covered Box and Whisker Plots. This included finding quartile 1, 2, 3 by using the median of the data set and the median of the two halves of the data set. We then worked on some test problems that included probability, finding volume, and solving word problems."

"The student felt he did well on his quiz last week. We worked from the book on possible future topics. We started with a review of sin and cos graph transformations. We then moved on to csc and sec graph transformations. He did well with the csc and sec graphs and seemed to have little trouble transferring his knowledge of cos and sin graphs to the new topic. Next, we covered tan and cot graphs with vertical & horizontal shifts as well as changes in period. After reviewing these graphs, he and I talked about how these functions (specifically sin and cos) are used to model 'real world' systems (springs, Ferris wheels, etc.). The final topic we worked through was inverse trig functions, i.e.. Arcsin, Arccos, Arctan, etc. Overall he seemed to understand the new material. He will continue to work through these topics over the course of next week during school. "