Quadratic Approximation
GROUP MEMBERS:
1. _____________________________
2. ______________________________
3. ______________________________
4. ______________________________
Goal: To calculate the quadratic approximation for f(x,y)= = x2 -4x + y2 -6y +1 near (x0=2, y0=3).
Q(x,y) = f(x0, y0) + fx (x0, y0) (x - x0) + fy (x0, y0) (y - y0) +
1/2 { fxx (x0, y0) (x - x0)2 + 2 fxy (x0, y0) (x - x0) (y - y0) + fyy (x0, y0) (y - y0)2 }
Person 1: Evaluate f(x,y) at (x0=2, y0=3).
Person 2: Calculate fx and evaluate at (x0=2, y0=3).
Person 3: Calculate fy and evaluate at (x0=2, y0=3).
Person 4: Calculate fxx and evaluate at (x0=2, y0=3).
Person 1: Calculate fxy and evaluate at (x0=2, y0=3).
Person 2: Calculate fyy and evaluate at (x0=2, y0=3).
Person 3: Using all these results, write down the quadratic approximation based at (x0=2, y0=3).
Q(x,y) =
Group: By looking at this formula, state the shape of the graph near the critical point (x0=2, y0=3). Classify the type of the critical point.