Final answer:
The linearization of the given function at (5, 2) can be found by calculating the partial derivatives and substituting them into the linearization formula. This will give us the approximate linear equation that represents the function near the point (5, 2).
Step-by-step explanation:
The linearization of a function f(x, y) at a point (a, b) is given by the equation:
l(x, y) = f(a, b) + fx(a, b)(x - a) + fy(a, b)(y - b)
In this case, the function f(x, y) = 403 - 2/(x3 - y0). To find its linearization at (5, 2), we need to calculate the partial derivatives of f with respect to x and y at that point. Then, we substitute these values into the equation above.
Let's calculate the partial derivatives:
- fx(x, y) = -6x2/(x3 - y0)2
- fy(x, y) = 0
Now, substitute a = 5, b = 2, x = 5, and y = 2 into the equation l(x, y) = f(a, b) + fx(a, b)(x - a) + fy(a, b)(y - b) to find the linearization.