HW: Review 3.5 - 3.9 should be done. Turn in homework on Thursday. Details are listed in IC. Test on Thursday, 2/2.

We went over WS 5.3 day 3 as well as Question #2 on the last page of WS 3.9 day 2 packet. Students worked on their quiz 5.3 & 3.9. Students will have 5 minutes to complete it.
HW: Review 3.5 - 3.9 should be done. Turn in homework on Thursday. Details are listed in IC. Test on Thursday, 2/2. Students received their Quiz 8.7 back and we went over questions. Then we discussed problems on the WS Derivative of Inverse Functions Gift. We also checked the problems on WS Derivative of Inverse Functions Homework (1 - 9). Lastly, we reviewed linearization by checking the multiple choice problems that were assigned last week.
HW: Complete WS 5.3 day 3 and WS Review on L'Hopital's Rule. Quiz tomorrow over 5.3 (derivative of inverse functions) and 3.9 (linearization). We started with a short 4 question review on L'Hopital's rule using Kahoot. Then we completed the classwork page on derivatives of inverse functions. Students then had about 17 minutes to complete their quiz.
HW: WS Derivatives of Inverse Functions GIFT (MC questions and answers on the last page), complete the Homework page of Derivatives of Inverse Functions & start working on reivew 3.5 - 3.9. Our first test will be next week. We started with a 7 question review of L'Hopital's rule using Kahoot. Then we reviewed some key concepts of inverse functions and completed 3 examples where we found the derivative of an inverse function. We looked at the graph of inverse functions and compared their slopes at the inverse points. We found that those slopes were opposite reciprocals. We showed how we could get the derivative of the inverse at the inverse point by either find the inverse or working off the main function and using its reciprocal at the inverse point.
Need more examples, check out these videos: http://www.youtube.com/watch?v=nSmFzOpxhbY http://www.youtube.com/watch?v=Lt0L3wDHqm8 Want to try some more problems? Use the link below http://archives.math.utk.edu/visual.calculus/3/inverse.1/index.html Use this 4 step process for the problems on the derivatives of inverse functions - homework. Step 1: determine the inverse point by setting f(x) = a (the given value) Step 2: find f'(x) Step 3: find f' (inverse point - you got this in step 1) Step 4: take the reciprocal (answer in step 3) HW: Quiz on L'Hopital's Rule tomorrow. WS Derivative of Inverse Functions - Homework (1 - 9) Students completed the homework and classwork on L'Hopital's rule. Great job was done!
Students received their quizzes back from yesterday. Groups had the last 5 - 10 minutes to revise 1 or 2 questioins. HW: Complete the second WS on L'Hopital's rule (1 - 8) and the back side a,b, and c. Students worked with a partner to complete the 4 question quiz on optimization. Then we learned about another way to find the limit IF the limit results in an indeterminate form (0/0 or infinity/infinity). We completed 5 examples together on the classwork sheet.
Use the link below for more examples. http://www.youtube.com/watch?v=Sp0G-VggAoU http://www.youtube.com/watch?v=PdSzruR5OeE http://www.khanacademy.org/math/calculus/derivative_applications/lhopital_rule/v/introduction-to-l-hopital-s-rule Additional practice: http://archives.math.utk.edu/visual.calculus/3/lhospital.1/i HW: Complete WS L'Hopital's Rule Homework (1 - 11). We went over 3 more examples of using linearization to approximate a given value. Students completed the first side of our 3.9 day 2 linearization worksheet. We also went over 3 problems from the Practice Quiz 3.7. We finished with an optimization question which found the point on y = (3x)^0.5 that was closest to the point (3, 0).
Use the link to review a similar optimization problem: https://www.youtube.com/watch?v=uGIOHXm_tfE HW: Complete 3.9 day 2 linearization worksheet 1 - 11 & quiz 3.7 is tomorrow. Students were given a 4 question 3.7 practice quiz. We started our examples on differentials; key point being that dy is the approximate change and not the actual change at a particular x-value and given change in x. The linearization is just the equation of the tangent line at that point (a, f(a)) where L(x) is isolated.
Good video on differentials and linear approximations: https://www.youtube.com/watch?v=CMeJYSvXKxc The link below has some more worked out examples (scroll down and you'll find them) http://www.cliffsnotes.com/math/calculus/calculus/applications-of-the-derivative/differentials HW: Complete the 4 question 3.7 practice quiz (answers are posted on the AP Calc page) and complete the 1 - 2 on the WS Linear Approximation Homework. Students received back their 3.6 quizzes. Then we used class time to discuss WS 3.7 Optimization (1 - 8) with tablemates and as a class. We worked out most of the problems in class. Students then had the remaining 10 minutes to work on the back (9 - 13).
HW: Complete WS 3.7 Optimization (1 - 13). Quiz 3.7 on Monday, 1/23. Students tackled the boat and ambulance problem. We showed how to use calculus to find the meeting place that minimizes the travel time for the patient. We also confirmed our work by examining the graph.
Students also completed their quiz 3.6. We had time to set up #1 and #4 on today's homework. HW: Complete WS 3.7 Optimization 1 - 8 all (make sure 1 - 4 is done from yesterday's worksheet). |
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