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Calculate ∂f ∂x , ∂f ∂y , ∂f ∂x (1, −1) , and ∂f ∂y (1, −1) when defined. (If an answer is undefined, enter UNDEFINED.) f(x, y) = 9,000 − 70x + 12y +7xy ∂f ∂x = Incorrect: Your answer is incorrect. ∂f ∂y = Incorrect: Your answer is incorrect. ∂f ∂x (1, −1) = Incorrect: Your answer is incorrect. ∂f ∂y (1, −1) = Incorrect: Your answer is incorrect.

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Answer:

[tex]\frac{\partial f}{\partial x} = -70+7\cdot y[/tex], [tex]\frac{\partial f}{\partial y} = 12+7\cdot x[/tex], [tex]\frac{\partial f}{\partial x} (1,-1) = -77[/tex], [tex]\frac{\partial f}{\partial y}(1,-1) = 19[/tex]

Step-by-step explanation:

Let [tex]f(x,y) = 9000-70\cdot x +12\cdot y +7\cdot x \cdot y[/tex], then the first partial derivatives of this multivariate function are, respectively:

[tex]\frac{\partial f}{\partial x} = -70+7\cdot y[/tex] (1)

[tex]\frac{\partial f}{\partial y} = 12+7\cdot x[/tex] (2)

Now we evaluate the partial derivatives at [tex](x,y) = (1, -1)[/tex]:

[tex]\frac{\partial f}{\partial x}(1,-1) = -70+ 7\cdot (-1)[/tex]

[tex]\frac{\partial f}{\partial x} (1,-1) = -77[/tex]

[tex]\frac{\partial f}{\partial y}(1,-1) = 12+7\cdot (1)[/tex]

[tex]\frac{\partial f}{\partial y}(1,-1) = 19[/tex]

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