Question

Let F(x, y)=30∛(x-y). If (x, y) changes from (2,1) to (2.201,0.87), find ΔF and dF.

Answer 1

To find ΔF and dF, we use the concept of partial derivatives. ΔF represents the change in F, while dF represents the infinitesimal change in F.

Step-by-step explanation:

To find ΔF and dF, we need to use the concept of partial derivatives. The partial derivative ∂F/∂x represents the rate of change of F with respect to x, while ∂F/∂y represents the rate of change of F with respect to y.

Using the given function F(x, y) = 30∛(x - y), we can calculate the partial derivatives as follows:

∂F/∂x = 30∛(x - y)1/3 / ∂x = 10(x - y)-2/3

∂F/∂y = 30∛(x - y)1/3 / ∂y = -10(x - y)-2/3

Now, to find ΔF and dF, we need to substitute the given values of (x, y). ΔF represents the change in F, while dF represents the infinitesimal change in F.