The height of a certain hill (in meters) is given byh(x,y)= 10 ( 2x y - 3 x^2- 4 y^2- 18 x + 28 y + 12),
where y is the distance (in kilometers) North, x the distance East
(a) How steep is the slope (in meters per kilometer) at a point 1 km north and 1 km east and in what direction is the slope the steepest at that point?
I know this has something to do with partial derivatives, but I am not 100% sure of the step proces..
I've calculated grad (http://www.mathhelpforum.com/math-he...fb9e51b8-1.gif), should I dot with the unit vector before evaluating, or should I evaluate grad at 1,1 then dot with unit vector?
I tried and returned an answer of 0, somehow I'm not convinced this is correct!
I found:
partial derivative of h with respect to x to be 20y - 60x - 180
and
partial derivative of h with respect to y to be 20x - 80y + 280
Evaluated at (1,1) these are -220 and 220 respectively.
Then the at (1,1) is (1/sqrt(2), 1/sqrt(2)).
Dotting gives (-220)(1/sqrt(2)) + (220)(1/sqrt(2)) yielding 0!
Where have I gone wrong?