Question

Find the linearization of the function z=x √y at the point (7 , 4). L(x, y)=2x+(7/4)y

Answer 1

The linearization of the function z=x √y at the point (7 , 4) is L(x, y) = 14 + (7/4)(y-4).

Step-by-step explanation:

To find the linearization of the function z=x √y at the point (7 , 4), we need to use the formula:L(x, y) = f(a, b) + f_x(a, b)(x-a) + f_y(a, b)(y-b)
Given that the point is (7, 4) and the function is z = x √y, we can substitute these values into the formula to get:
L(x, y) = 2(7) + (7/4)(y-4)
Simplifying, we get:
L(x, y) = 14 + (7/4)(y-4)
Therefore, the linearization of the function at the point (7, 4) is L(x, y) = 14 + (7/4)(y-4).