Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 5 sin(xy), (0, 2) maximum rate of change Incorrect: Your answer is incorrect. direction vector

Answer with Step-by-step explanation:

We are given that

Point=(x,y)=(0,2)

We have to find the maximum rate of change of f at given point.

Maximum rate of change of f at point (0,2)=

Where x=Coefficient of i

y=Coefficient of j

By using the formula

Maximum rate of change of f at point (0,2)=

Direction of maximum rate of change of f=

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step-by-step explanation:

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c