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Karolina [17]
2 years ago
5

Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 9 sin(xy), (0, 8)

Mathematics
1 answer:
malfutka [58]2 years ago
3 0

Answer:

The magnitude is  \Delta f(0,8)  =  72

The  direction  is  i i.e toward the x-axis

Step-by-step explanation:

From the question we are told that

   The function is  f(x, y) =  9sin(xy) \ \ \

    The point considered is  (0,8 )

Generally the maximum rate of change of f at the given point and the direction is mathematically represented as

            \Delta f(x,y) =  [\frac{\delta  f(x,y)}{\delta x } i + \frac{\delta  f(x,y)}{\delta y } j  ]

             \Delta f(x,y) =  [\frac{\delta  (9sin(xy))}{\delta x} i  + \frac{\delta  (9sin(xy))}{\delta y} i   ]

            \Delta f(x,y) = [9y cos (x,y) i +  9xcos (x,y) j]

At  (0,8 )

            \Delta  f (0,8) =  [9(8) cos(0* 8)i  + 9(8) sin(0* 8)j  ]

            \Delta  f (0,8) = 72 i

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