Suppose that f(x, y) is a smooth function and that its partial derivatives have the values, fz(5,8) = 2 and fy(5, 8) = -4. Given that f(5, 8) = 6, use this information to estimate the value of f(6,9). Note this is analogous to finding the tangent line approximation to a function of one variable. In fancy terms, it is the first Taylor approximation. Estimate of (integer value) f(5,9) Estimate of (integer value) f(6,8) Estimate of (integer value) f(6,9) B

Q: The cost (in dollars) of manufacturing one item is given by C(x, y) = 70 + 4x + 9y where x is the…

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Q: 2. Find the gradient of the function f(x, y) = ln(x² + y²) at the point(1, 1).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If f(x, y, z) 2x5 + 3y5 - 8x2y2z2, what is the partial derivative of f with respect to z?

A: The given function is fx, y, z=2x5+3y5-8x2y2z2.

Q: Find the partial derivative of the given In[y? sec(x²y²)].

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Q: Explain in a sentence what the partial derivative of f with respect to x represents in the context…

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Q: Find both first partial derivatives, as well as fy for

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Q: xy Find all second order derivatives for r(x,y)= 4x +9y

A: The given function is

Q: A.   Note on Jacobian dterminants and also give economic interpretation of total differentiation.…

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Q: The partial derivative fx(-1,0) of ƒ(x, y) = xe³ + x² + 1 is equal to −1. Select one: True False

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Q: f(x, y) = 2cos(2x-9y) and g(x, y) = -9cos(2x-9y). af ду og dx The partial derivatives and are equal.…

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Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: Find all three of the partial derivatives for the profit function; P (m, r, g)  = rg – m –…

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Q: az x²+y² - z² = 2x( y + z) ; 江一下

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Q: Solve the partial differentiabion equation +6.0 = 2-y Ox Show that the gereral aoludion 2.

A: Given. the partial differential equation                            ∂2z∂x2+5∂2z∂x∂y+6∂2z∂y2=2x-y…

Q: If the derivative of an analytic function f is 0, does that mean that the partial derivative of f…

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Q: If f(x, y) = x3 + y4, what is the partial derivative of f with respect to х? .A fx = 4x3 || .B fx =…

A: The objective is  to find the partial derivative with respect to x.

Q: (b) Find all first and second partial derivatives of z = x² In(x² + xy).

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…