## polar partial derivative

1.

suppose that f(1,2) = 2, fx (1,2) = 3, fy(1,2) = -4, fxx(1,2) = 7, fxy = 8, fyy = 6

a.) find fr and f-theta at x = 1 , y = 2 where r, theta are polar coordinates

b.) find the minimum value of f for all points within a circle of radius 0.1 about x = 1, y = 2. At what point does the minimum occur. I answered at point (1,2.1) with the value of 1.6 due to the fact that fy is faster than fx and thus it has to be at the point where there is the greatest increasing y which is (1.21)....am I correct?

c.) show that if you head in the direction in which f increases at the greatest rate, then fy remains constant O.o wtflol

2. find the smallest distance from P = (2,3,5) to the line through Q = (1,4,-1) and R = (2,4,6)