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Multivariable CalculusMediumPartial Derivatives & the Gradient

Partial Derivatives & the Gradient · Medium problem

Let f(x,y)=x3−xy2f(x,y) = x^{3} - xy^{2}. Use the linear approximation of ff at (3,2)(3,2) to estimate f(3.1, 1.8)f(3.1,\ 1.8), then find how much that estimate differs from the true value of f(3.1,1.8)f(3.1,1.8) (estimate minus true value). Give an exact answer as a decimal.