- Typo in chain rule problem set: problem 3 should be section 3.7 exercise 2
- (Online version is fixed now)
- Section 3.8
- Strategy (6 steps)
- Picture
- Write down what you want
- Rate is derivative
- Write equation between variables
- Differentiate wrt t (time)
- Evaluate
- Often use chain rule
- Strategy (6 steps)
- Examples
- Pedestrian and car
- What sort of related rates problem(s) arise here?
- Rate at which distance between pedestrian and car is narrowing is a good one
- Rate at which distance between pedestrian and car is narrowing is a good one
- Figure out actual rate at which distance is closing when pedestrian is
10 feet from crosswalk, car 50. Use R to keep intermediate results
in variables.
> x = 10 /5280 > x [1] 0.001893939 > y = 50 / 5280 > y [1] 0.009469697 > ( 4*x + 15 * y ) / sqrt( x^2 + y^2 ) [1] 15.49317 > s = 15.49317 * 5280 > s [1] 81803.94 > s / 60 [1] 1363.399
- What sort of related rates problem(s) arise here?
- Cat and spot of light
- How fast is spot moving as person rotates reflector?
- Or how fast is spot moving if person holds reflector at constant angle but raises their hand?
- Sliding weight on rotating arm
- Pedestrian and car
- Problem set
- Sliding weight rate problem
- Estimating with derivatives