Find the maximum rate of change of f(x, y)=ln(x2+y2) at the point (-2, 2) and the direction in which it occurs.

Step-by-step explanation:

Maximum rate of change of a function f(x,y) is expressed as the gradient of such function at the given point. Gradient of a function is expressed as;

∇f(x,y) =

Given f(x,y)=ln(x²+y²) at the point (-2, 2)

Hence the maximum rate of range of the function at the point (-2,2) is

To get the direction, we willl use the formula;

From the vector gotten, x = -1/2 and y = 1/2

Since tan theta is negative in the second quadrant, the direction in which it occurs will be 180-45 = 135°

i would need to see the dot plot : )

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb