the pond to remain constant? The depth of a pond at the points with coordinates (x,y) is given by h(x,y)=2x^2+3y^2 feet.
(a) If a boat at pt(-1,2) is sailing in the direction of the vector <4,1>, is the water getting deeper or shallower? At what rate? Assume that x and y are measured in feet.
(b) In which direction should the boat travel at (-1,2) move for the depth to remain constant?
(a) I found the partial derivatives fx=4x and fy=6y, so heading in a positive x and positive y direction such as along vector <4,1> would mean z gets more positive and therefore the pond is getting shallower. Is this enough justification/ is there a better way to work through this problem?
(b) This is my main question... I think it has something to do with the boat traveling along the contour of the pond???
Thank you!
(a) If a boat at pt(-1,2) is sailing in the direction of the vector <4,1>, is the water getting deeper or shallower? At what rate? Assume that x and y are measured in feet.
(b) In which direction should the boat travel at (-1,2) move for the depth to remain constant?
(a) I found the partial derivatives fx=4x and fy=6y, so heading in a positive x and positive y direction such as along vector <4,1> would mean z gets more positive and therefore the pond is getting shallower. Is this enough justification/ is there a better way to work through this problem?
(b) This is my main question... I think it has something to do with the boat traveling along the contour of the pond???
Thank you!