Section 4.7 Worksheet:

Fall break issue

Assigned problems: Exercises pp. 282-287, #4, 5, 6, 12, 28, 29, 34, 36, 40 (due Friday).

1. Write a haiku or limerick involving any of the words ``extrema(um)'', ``minima(um)'', ``maxima(um)'', or ``optimization''. If it's really good, email it to me! (There will be a prize for first place....)

2. Why does the 1st derivative test for absolute extreme values make perfect sense? (Explain in your own words!)

3. Does the 1st derivative test for absolute extreme values require that f be differentiable at c? If not, give an example that illustrates this; if so, give an example that illustrates the theorem.

4. While home on fall break, slice a banana while scrupulously avoiding any thoughts of orthogonality.

5. (This problem requires the use of dangerous projectiles. Please use extreme caution!) While home on fall break, cross a busy street while scrupulously avoiding any thoughts of orthogonality....

Notes:

1. While we're skipping section 4.6, there are a few words of caution which we might gather from it.

   While calculators are a great boon to us, it's still possible to rely too heavily on them, and to fail to rely on ourselves and our own understanding. For example, calculus gives us an idea of where the interesting behavior of a function is occurring, which indicates a domain and a range wherein a nice graphical representation can be obtained.

   Sometimes a function cannot be well represented on a single graph (for example, there may be two different ranges in which the function operates, and it may not be possible to see both at the same time (for example, how could you have a picture of the whole oak tree and the individual acorns on the branches?).