- Hour exam 2
- Friday (Nov. 14)
- Covers material from 1st exam through optimization (e.g., chain rule, implicit differentiation, related rates, Mean Value Theorem, curve sketching, extrema and optimization, etc.)
- 6 - 9 short answer questions, including word problems
- Rules and format otherwise similar to 1st exam, especially open references rule
- Related rates procedure?
- (Understand the problem e.g., “given …, find rate of…”)
- Write equation(s) to relate what you want to knowns
- Differentiate to get desired rate
- Plug in known values to get number for desired rate
- Problem set question 2
- Sketch of (x3 + x - 2)/(x-x2)
- = (x3 + x - 2)/(x(1-x))
- (1-x) divides numerator
- Moral: if you get into a problem and find it way more complicated than you like, take a minute to think about whether there’s a way to make it simpler
- Optimization example?
- What’s the shortest route for explorer at base of
parabolic peninsula to shore?
- What’s the shortest route for explorer at base of
parabolic peninsula to shore?
- (After exam)
- Sums and definite integrals
- Read section 5.2