Vector Analysis:Differential Calculus 1. The problem statement, all variables and given/known data The height of a certain hill(in feet) is given by h(x,y)=10(2xy-3x^2-4y^2-18x+28y+12) where y is the distance (in miles) north, x the distance east of South Hadley a)Where is the top of the hill located b) How high is the hill? 2. Relevant equations grad T=dT/dx xhat+dT/dy yhat+ dT/dz zhat 3. The attempt at a solution a) I need to find the distance in the x direction , so I would take the derivative of h(x,y) with respect to x dh/dx=20*x-12=0=> x=3/5 feet b) same algorithm, only I am now ask to calculate how high the hill is and so I would take the derivative of h(x,y) with respect to y: dh/dy=y=3*x+9=3*(.6)+9=10.8 feet or maybe I should calculate h(x,y) in order to determine the height of the hill. Therefore , I'd plugged x and y into h(x,y) right?