- Colloquium
- “The Single Distance Problem”
- Dr. Michael Bennett (Geneseo math alum, Ph. D f/ UR(?), now at RIT)
- Wednesday, Nov. 4, 2:45, Newton 204
- Extra credit as usual
- Due dates for problem set 8 (extreme values)
- Complete by Friday, Nov. 6
- Grade by Wednesday, Nov. 11
- Saddle points?
- A multivariable analog of inflection points, i.e., points where
derivatives are 0 without the function having a maximum or minimum
- A multivariable analog of inflection points, i.e., points where
derivatives are 0 without the function having a maximum or minimum
- Section 14.8
- Optimization
- You make, have, etc. f(x,y,z,...) units of something
- Subject to constraints g(x,y,z,...) = 0 on x, y, z, …
- What is maximum/minimum f?
- Ideas
- grad f = lambda grad g
- lambda = scalar coefficient
- grad f orthogonal to v at certain point
- grad f = lambda grad g
- Optimization
- Example
- Largest area rectangle enclosable with 100 feet of string?
- This is also a classic single-variable optimization problem; doing it that way yields same result as method of Lagrange multipliers used here
- Largest volume box enclosable in 100 square feet of metal?
- Analogous to above problem, but needs Lagrange multipliers
- Gradients give you equations from which you can cancel lambdas to get x = y, y = z, from which you can find x = y = z = √(100/6)
- Analogous to above problem, but needs Lagrange multipliers
- Largest area rectangle enclosable with 100 feet of string?
- Integration and multivariable functions
- Read section 15.1