1. The problem statement, all variables and given/known data (i) Drawing a contour map for the function h(x.y) = -12-4x^2+16x-y^2-8y (ii) (Continuing from i) at the point (1,-1,7) which direction to move to have the maximum increase in height? (iii) Find the point closest to the origin on the curve of intersection of the plane 2y + 4z = 5 and the cone z^2= 4x^2 + 4y^2. 2. Relevant equations (i) z = -12-4x^2+16x-y^2-8y (then Im stuck) (iii) I got f = z <--(not sure if this is right), g = 2y +4z = 5 and h = z^2= 4x^2 + 4y^2. then gradient f = lambda * gradient g + mu * gradient h 3. The attempt at a solution then from some caluculation i got two intersection point of (0,5/18,5/9) and (0, 1/10, 1/20) with (0, 1/10, 1/20) the point closest to the origin.