find absolute extrema & Lagrange Multipliers
1. given: f(x,y) = x^3 - 6xy + y^2 +15x
find absolute extrema of f over the triangluar region in the xy plane with vertices (0,0), (0,4) & (2,4).
2. given: T(x,y,z)=100+x^2 + y^2 represent the temperature at each point on the sphere x^2 + y^2 + z^2 =50. Use Lagrange Multipliers to find the Maximum & Minimum temperature on the curve formed by the intersection of the sphere and the plane x - z = 0. (hint: Optimizing a function subject to two constraints)
thanks for your big help....!