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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?

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# Homework Help: Vector Analysis ifferential Calculus

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