- Due dates for problem set 8 (extreme values)
- Complete by Friday, Nov. 6
- Grade by Wednesday, Nov. 11
- Hour exam 2 Monday (Nov. 2)
- Material since 1st hour exam (e.g., curvature, multivariable functions, partial
derivatives, gradient, directional derivatives, tangency, linearization, etc.)
- Sections 13.4, 14.1 - 14.6
- Rules and format otherwise similar to 1st hour exam (esp. open reference materials)
- Material since 1st hour exam (e.g., curvature, multivariable functions, partial
derivatives, gradient, directional derivatives, tangency, linearization, etc.)
- f(x,y) = 3x2 + xy + 2y2 + x - y + 7 has a minimum at ( -5/23, 7/23 )
- muPad as a tool to confirm
- Assigning numeric values to variables in an expression lets muPad “simplify” the expression into a single number, i.e., evaluate the expression
- Use
deletecommand to remove values from variables so they behave symbolically again
- muPad as a tool to confirm
- Extrema of f(x,y) = √(4 - x2 - y2)
- Partial derivatives find extrema inside function domain
- Boundary has to be handled somehow else
- In this case we can tell by inspection that f(x,y) = 0 everywhere on boundary
- In this case we can tell by inspection that f(x,y) = 0 everywhere on boundary
- What about same function over the triangle (0,0), (1,0), (0,1)?
- (After exam)
- Optimization problems and Lagrange multipliers
- Read section 14.8