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**1. Homework Statement**

(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. Homework 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.