Suppose that the height of a hill above sea level is given by z= 1000 -0.01x2 – 0.02y2. if you are at the point (60,1000) in what direction is the elevation changing fastest? What is the maximum rate of change of the elevation at this point?

Question

Suppose that the height of a hill above sea level is given by z= 1000 -0.01x2 – 0.02y2. if you are at the point (60,1000) in what direction is the elevation  changing fastest? What is the maximum rate of change of the elevation at this point?

Damon · Answer

z = 1000 - .01 x^2 - .02 y^2 dz = -.02 x dx -.04 y dy dz= -.02(60)dx - .04(1000)dy dz = -1.2 dx - 40 dy move in y direction , about 40 times as effective as x motion dz/dy = -40