Find the maximum rate of change of f(x, y, z) = x+y/z at the point (1, -3, 5) and the direction in which it occurs. Maximum rate of change: Direction (unit vector) in which it occurs: 000

4) For the function p = x?y + yz at the point (1,2,-1), find its rate of change with distance in the direction å = i+ 2j + 3k. At this same point, what is the greatest possible rate of change with distance and in which direction does it occur? マ.(マ×)

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The temperature at a point (x, y, z) is given by the following equation where T is measured in ºC and x, y, z in meters. T(x, y, z) = 200e-x²-3y²-9z² (a) Find the rate of change of temperature at the point P(2, -1, 2) in the direction towards the point (3, -3, 3). -10400 43√6 °C/m (b) In which direction does the temperature increase fastest at P? <-2, 3 -18 (c) Find the maximum rate of increase at P. -43 400e 3√337

Find the gradient of v number

Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, Y) = 3y?/x, (2, 6) maximum rate of change direction

explain the process of finding the normal vector using gradient

Find the average rate of change of between the points on the function whose coordinates are (1, 3), and (2, 16). (Enter an exact number.)