Use Lagrange multipliers to find the points on the given sur

Solution

I am not going to explain in detail exactly how to do this because I am sure that there are plenty of sties on the web that can help you understand Lagrange multipliers better than I can teach them myself, but basically: you have one equation: 17x^2+12xy+8y^2-100=0 (we\'ll call this f) and a constraint: (the distance formula) (x^2 + y^2)^(1/2)=0 (we\'ll call this g) if you set these each other so that the i-component of the gradient of f = the i component of the gradient of g * lambda (l. multiplier) and the j-component of the gradient of f = the j component of the gradient of g * lambda (l. multiplier) and you also have the equation (x^2 + y^2)^(1/2)=0 then solve for all possibilities of x and y once you find these values, plug them into your original equation, f and evaluate which ones are local minima/maxima