Respuesta :
The maximum rate of change of f at the given point is 0.3678
Rate of change
Rate of change defined as the percentage change in value over a defined period of time, and it represents the momentum of a variable.
Given,
Here we the function f(x, y) = [tex]xe^{-y}[/tex], (1, 0)
Now, we need to find the the maximum rate of change of f at the given point.
We know that, the average rate of change of f(x) on the interval [a, b] is written as,
=> f(x) = (fb) - f(a)/ b - a
Here the value of a = 1 and b = 0.
So, apply the values on the function to solve it,
f(1,1) = 1e⁻¹
f(1,1) = 1 x 0.3678
f(1,1) = 0.3678
Similarly, the value of f(0,0) is,
=> f(0,0) = 0e⁰
=> f(0,0) = 0 x 1
=> f(0,0) = 0
So, the rate of change is,
=> R = 0 - 0.3687/0-1
=> R = 0.3678.
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