AP: Warm-up problem comparing related rates to instantaneous rates and average rates. Went over homework problems. Remember that take-home test is due Wednesday. Show all work. Handed out a related rates packet. Choose 15 problems to do (excluding 1-4, 18, 20, 36-42). Due Friday. Notes
Honors: Finished all trig derivatives. Now we know slope functions of sin/cos/tan/csc/sec/cot. Also talked about differentiability and its connection to continuity. A continuous function isn't necessarily differentiable, but a differentiable function has to be continuous. If F is continuous and F' is continuous, then F' is differentiable. If F' is not continuous, then F is not differentiable. Finish piecewise derivative graphs packet for Wednesday. Notes
Tuesday
AP: Played the Tangent Lines game. Good practice on a useful skill. Began unit on velocity and acceleration, handed out Velocity packet. Remember the take home test is due tomorrow, and the related rates problems are due Friday. Notes on position/velocity/acceleration intro.
Wednesday
AP: Turned in our derivatives take home test. Worked through a velocity problem when the graph of v(t) was provided. Many were out of DS for various reasons, so nothing critical was discussed, just more examples.
Thursday
AP: More on position-velocity-acceleration. Discussed significance of negative velocities. Worked on a problem where the velocity (and an initial position) were provided and we figured out the original position function. Worked through some rectilinear motion problems (AP free response) wherein a particle moves along a line, often following a trigonometric function. Lecture notes
Homework: finish related rates packet for tomorrow. Review videos here:
cone, ladder, radius and area, balloon height, another circle
Friday
AP: Related rates packet due turned in. Examined applications of acceleration type problems involving generic graphs. Also looked at an economics problem using the derivative as "marginal cost". Notes
Homework: from the "Velocity" packet: 6, 8, 9, 24, 28.
Honors: More optimization examples. Basic procedure:
1. Draw a picture, assign variables.
2. Translate any given information into equations using those variables.
3. Establish which function will be optimized.
4. Make sure this function is expressed in only one variable. Substitute some restriction in to do so, if needed.
5. Take the derivative of the function to be optimized.
6. Set this derivative equal to zero and solve.
7. Be sure to report the answer you are being asked about.
Notes
Homework: Optimization handout: #3, 5, 6, 9