We have :
x^2+xy+y^2=3 and
y^2+yz+z^2=16
A=xy+yz+zx
Find the maximum value of
A.
Find x, y and z when A=max value.
(Remember the category)
(In reply to
re(2): Oooo... Getting schmancy, are we? by levik)
Short for gradient. If you have a function in the form R^n -> R^1 (that is, it takes multiple inputs and spits out a single number), then you can take the gradient of the function. The gradient of a function is another function in the form R^n -> R^n. In 3d space, it will take in a 3d vector and spit out another 3d vector.
The way to calculate a gradient is to take the partial derivative of the input function with respect to each of its inputs in turn. The results you get are the components of the gradient vector.
For a 1D function, the gradient is just the derivative of the function. If you have a 2D function that you visualize as a wavy surface, the gradient points in the uphill direction and the length of the gradient measures how steep the surface is at that point.
re(3): Oooo... Getting schmancy, are we?
