A function of two variables is given by,
f (x,y) = 4x^3 + 7xy^4 - 5y^2 + 8
Determine, fxx + fyx at x = 4.25 and y = 3.69,
giving your answer to 3 decimal places.
fx = 12x^2 + 7y^4
fy = 28xy^3 - 10y
fxx = 24x
fyx = 28y^3
plug in the numbers
thanks for helping me. i was stuck trying to solve this.
To determine fxx + fyx at x = 4.25 and y = 3.69, we need to calculate the second order partial derivatives of the function and substitute the given values.
The first step is to find the first order partial derivatives:
fx = d/dx (4x^3 + 7xy^4 - 5y^2 + 8)
= 12x^2 + 7y^4
fy = d/dy (4x^3 + 7xy^4 - 5y^2 + 8)
= 28xy^3 - 10y
Next, we find the second order partial derivatives:
fxx = d/dx (12x^2 + 7y^4)
= 24x
fyx = d/dy (12x^2 + 7y^4)
= 28y^3
Now, we substitute x = 4.25 and y = 3.69 into the derivatives:
fxx + fyx = 24(4.25) + 28(3.69)
= 102 + 102.92
= 204.92
Therefore, fxx + fyx at x = 4.25 and y = 3.69 is approximately equal to 204.92, rounded to three decimal places.