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Marianna [84]
3 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) = 5 sin(xy), (0, 2) maximu

m rate of change Incorrect: Your answer is incorrect. direction vector
Mathematics
1 answer:
Ahat [919]3 years ago
7 0

Answer with Step-by-step explanation:

We are given that

f(x,y)=5 sinxy

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

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

f_x(x,y)=5ycos(xy)

f_x(0,2)=5(2)cos0=10

f_y(x,y)=5xcosxy

f_y(0,2)=5(0)cos0=0

\Delta f(0,2)=f_x(0,2)+f_y(0,2)=10i+0j

Maximum rate of change of f at point (0,2)=\mid \Delta f(0,2)\mid=\sqrt{x^2+y^2}

Where x=Coefficient of i

y=Coefficient of j

By using the formula

Maximum rate of change of f at point (0,2)=\sqrt{(10)^2+0}=10

Direction of maximum rate of change of f=\Delta\har{f}=\frac{\Delta f(0,2)}{\mid\Delta f(0,2)\mid}=\frac{10i}{10}=i

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