Question

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 1

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=$\Delta\har{f}=\frac{\Delta f(0,2)}{\mid\Delta f(0,2)\mid}=\frac{10i}{10}=i$