- No quiz this week: we'll be reviewing on Wednesday.
- Regarding IMath assignments: some of you have taken me up on my offer to re-open IMath assignments.
Email me with your requests for any that you want to try (tell me which assignments you want re-opened).
NB: Please don't pay any attention to your percentage score on IMath. Each assignment is equally weighted.
- On Wednesday we'll review; come with questions!
- We worked on section 3.3: Global optimization
- Your quiz covered section 3.5: Related Rates. You might have
noticed that I gave you the second problem from our worksheet
(which we did not discuss -- we did 1 and 3 together).
- A lot of you realized that the solution would involve the Pythagorean theorem. Some of you went for the angle, but we're asking about the rate of change of the distance between them -- so, right away, identify the "distance between them" as the quantity of most importance.
- Your solution has got to involve derivatives, right? If you don't see a derivative anywhere, you know that you're in trouble....
- At the end of my favorite soltion strategy -- UPCE, or
"oopsy!" -- is "E for evaluate": think about your
answer, and ask "does it make sense?".
(UPCE is "Understand, Plan, Carry out, Evaluate.)
In this case, you might consider a special case: if the two were moving away from each other at the same speed, say 55 mph, and started equidistant from the origin, then the triangle would be right isosceles, and the diagonal would be growing at \(\sqrt{2}\)*55 -- at a speed greater than either one alone.
More generally, the hypothenus has to grow faster than either leg alone.
- Key
- I gave you a worksheet for 3.3;
we'll see if we can get back to that after we cover our new
material.
- Today our new topic is Section
3.4: Applied Optimization (and it's our last section!).
- Applied optimization is exactly what you might expect: we're
looking at "real problems", and attempting to crack them using
tools from calculus.
- Our authors have their own
version of UPCE, which is a little more specific to these
types of optimization problems.
- We'll focus on one example in this section, Activity
3.4.3, only in a slightly different context. While the
problem is stated in the context of a hiker, we'll do what is
effectively the same problem, only to demonstrate that a dog
does calculus!
- Do
Dogs Know Calculus? Certainly they do; they just don't
know they do!
Nature is very particular about choosing optimal paths, and so Elvis, creature of nature, is pretty good about doing so (even if he can't state the Extreme Value Theorem).
- How about a worksheet? Your last one...
- Applied optimization is exactly what you might expect: we're
looking at "real problems", and attempting to crack them using
tools from calculus.
- Do Dogs Know Calculus?
- Cherry
blossoming data (from the EPA). Some "Key Points" cited in that webpage:
- Based on the entire 102 years of data, the average peak bloom date for Washington's cherry blossoms is April 4.
- Peak bloom date for the cherry trees is occurring earlier than it did in the past. Since 1921, peak bloom dates have shifted earlier by approximately seven days. The peak bloom date has occurred before April 4 in 16 of the past 20 years.
- While the length of the National Cherry Blossom Festival has continued to expand, the Yoshino cherry trees have bloomed near the beginning of the festival in recent years. During some years, the festival missed early peak bloom dates entirely.
- More generally, Leaf and Bloom Dates (EPA)