Vector Calc: in which direction should a boat travel for the depth of

StarMoon

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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!
 
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