[SOLVED] Find ∂f/∂x and ∂f/∂y for

> Kraft Foods successfully introduced DiGiorno Pizza into the marketplace in 1996, with first-year sales of $120 million, followed by $200 million in sales in 1997. It was neither luck nor coincidence that DiGiorno Pizza was an instant success. Kraft condu

> Give a specific example of data that might be gathered from each of the following business disciplines: accounting, finance, human resources, marketing, information systems, production, and management. An example in the marketing area might be “number of

> Refer to Example 3. If labor costs $100 per unit and capital costs $200 per unit, express as a function of two variables, C(x, y), the cost of utilizing x units of labor and y units of capital.

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f (x, y) at each of these points. If the second-derivative test is inconclusive, so state. f (

> Consider the Cobb–Douglas production function f (x, y) = 20x1/3y2/3. Compute f (8, 1), f (1, 27), and f (8, 27). Show that, for any positive constant k, f (8k, 27k) = k f (8, 27).

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f (x, y) at each of these points. If the second-derivative test is inconclusive, so state. f (

> Both first partial derivatives of the function f (x, y) are zero at the given points. Use the second-derivative test to determine the nature of f (x, y) at each of these points. If the second-derivative test is inconclusive, so state. f (x, y) = 1/x + 1/

> Both first partial derivatives of the function f (x, y) are zero at the given points. Use the second-derivative test to determine the nature of f (x, y) at each of these points. If the second-derivative test is inconclusive, so state. f (x, y) = y ex - 3

> Both first partial derivatives of the function f (x, y) are zero at the given points. Use the second-derivative test to determine the nature of f (x, y) at each of these points. If the second-derivative test is inconclusive, so state. f (x, y) = x4 - 4xy

> Both first partial derivatives of the function f (x, y) are zero at the given points. Use the second-derivative test to determine the nature of f (x, y) at each of these points. If the second-derivative test is inconclusive, so state. f (x, y) = 2x2 - x4

> Both first partial derivatives of the function f (x, y) are zero at the given points. Use the second-derivative test to determine the nature of f (x, y) at each of these points. If the second-derivative test is inconclusive, so state. f (x, y) = 6xy2 - 2

> Both first partial derivatives of the function f (x, y) are zero at the given points. Use the second-derivative test to determine the nature of f (x, y) at each of these points. If the second-derivative test is inconclusive, so state. f (x, y) = 3x2 - 6x

> The function f (x, y) = 1/2 x2 + 2xy + 3y2 - x + 2y has a minimum at some point (x, y). Find the values of x and y where this minimum occurs.

> Find a formula C (x, y, z) that gives the cost of material for the rectangular enclosure in Fig. 7(b), with dimensions in feet. Assume that the material for the top costs $3 per square foot and the material for the back and two sides costs $5 per square

> The function f (x, y) = 2x + 3y + 9 - x2 - xy - y2 has a maximum at some point (x, y). Find the values of x and y where this maximum occurs.

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = x4 - 2xy - 7x2 + y2 + 3

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = x3 + x2y - y

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = x4 - 8xy + 2y2 - 3

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = 1/3 x3 - 2y3 - 5x + 6y - 5

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = 15/4 x2 + 6xy - 3y2 + 3x + 6y

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = 2x3 + 2x2y - y2 + y

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = -8y3 + 4xy + 4x2 + 9y2

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = -8y3 + 4xy + 9y2 - 2y

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = x2 - y3 + 5x + 12y + 1

> Find a formula C (x, y, z) that gives the cost of materials for the closed rectangular box in Fig. 7(a), with dimensions in feet. Assume that the material for the top and bottom costs $3 per square foot and the material for the sides costs $5 per square

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = x3 + y2 - 3x + 6y

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = 4x2 + 4xy - 3y2 + 4y - 1

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = 3x2 + 8xy - 3y2 - 2x + 4y - 1

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = -3x2 + 7xy - 4y2 + x + y

> Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = x2 - 5xy + 6y2 + 3x - 2y + 4

> Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = ex/(1 + ey)

> Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = (2x - y + 5)2

> Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = 1/(x + y)

> Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = x/y + y/x

> Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = x exy

> Let f (x, y) = xy. Show that f (2, 3 + k) - f (2, 3) = 2k.

> Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = 2x2ey

> Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = x2 - y2

> The productivity of a country is given by f (x, y) = 300x2/3y1/3, where x and y are the amount of labor and capital. (a) Compute the marginal productivities of labor and capital when x = 125 and y = 64. (b) Use part (a) to determine the approximate effec

> A farmer can produce f (x, y) = 200 √(6x2 + y2) units of produce by utilizing x units of labor and y units of capital. (The capital is used to rent or purchase land, materials, and equipment.) (a) Calculate the marginal productivities of labor and capita

> Let f (x, y) = xey + x4y + y3. Find ∂2f/∂x2, ∂2f/∂y2, ∂2f/∂x∂y, and ∂2f/∂y∂x.

> Let f (x, y) = x3y + 2xy2. Find ∂2f/∂x2, ∂2f/∂y2, ∂2f/∂x∂y, and ∂2f/∂y∂x.

> Let f (x, y) = x/(y – 6). Compute ∂f/∂y (2, 1) and interpret your result.

> Let f (x, y) = xy2 + 5. Evaluate ∂f/∂y at (x, y) = (2, -1) and interpret your result.

> Let f (x, y) = (x + y2)3. Evaluate ∂f/∂x and ∂f/∂y at (x, y) = (1, 2).

> Let f (x, y) = xy. Show that f (2 + h, 3) - f (2, 3) = 3h.

> Let f (x, y) = x2 + 2xy + y2 + 3x + 5y. Find ∂f/∂x (2, -3) and ∂f/∂x (2, -3).

> Let f (x, y, z) = xy/z. Find ∂f/∂x, ∂f/∂y, and ∂f/∂z.

> Construct angles with the following radian measure. -π

> Determine the radian measure of the angle shown.

> Evaluate the given integral. ∫0 π/4 (2 + 2 tan2 x) dx

> Let f (x, y, z) = xz eyz. Find ∂f/∂x, ∂f/∂y, and ∂f/∂z.

> Evaluate the given integral. ∫0 π/4 tan2 x dx

> Evaluate the given integral. ∫ (2 + tan2 x) dx

> Evaluate the given integral. ∫ (1 + tan2 x) dx

> Evaluate the given integral. ∫ tan2 3x dx

> Evaluate the given integral. ∫ tan2 x dx

> Find the average of the function f (t) over the given interval. f (t) = cos t + sin t, - π ≤ t ≤ 0

> Find the average of the function f (t) over the given interval. f (t) = 1000 + 200 sin 2 (t - π /4), 0 ≤ t ≤ 3 π /4

> Find the average of the function f (t) over the given interval. f (t) = t - cos 2t, 0 ≤ t ≤ π

> Find the average of the function f (t) over the given interval. f (t) = 1 + sin 2t – 1/3 cos 2t, 0 ≤ t ≤ 2π

> In Fig. 2: Find the shaded area A4. Figure 2: 1 Y 0 A₁ cosx TU2 A3 sin x X

> Let f (x, y, z) = zex/y. Find ∂f/∂x, ∂f/∂y, and ∂f/∂z.

> In Fig. 2: Find the shaded area A3. Figure 2: 1 Y 0 A₁ cosx TU2 A3 sin x X

> In Fig. 2: Find the shaded area A2. Figure 2: 1 Y 0 A₁ cosx TU2 A3 sin x X

> In Fig. 2: Find the shaded area A1. Figure 2: 1 Y 0 A₁ cosx TU2 A3 sin x X

> Evaluate the following integrals. ∫ 2 sec2 2x dx

> Evaluate the following integrals. ∫ sec2 x/2 dx

> Evaluate the following integrals. ∫-π π (cos 3x + 2 sin 7x) dx

> Evaluate the following integrals. ∫0 π (x - 2 cos (π - 2x))

> Evaluate the following integrals. ∫ cos (6 - 2x) dx

> Evaluate the following integrals. ∫0 π /2 cos 6x dx

> Evaluate the following integrals. ∫ (3 cos 3x - 2 sin 2x) dx

> Let f (x, y, z) = (1 + x2y)/z. Find ∂f/∂x, ∂f/∂y, and ∂f/∂z.

> Evaluate the following integrals. ∫ sin (π - x) dx

> A spirogram is a device that records on a graph the volume of air in a personâs lungs as a function of time. If a person undergoes spontaneous hyperventilation, the spirogram trace will closely approximate a sine curve. A typical trace

> Find the area of the region bounded by the curves y = x and y = sin x from x = 0 to x = π.

> Find the area of the region between the curve y = cos t and the t-axis from t = 0 to t = 3π/2.

> Find the area of the region between the curve y = sin t and the t-axis from t = 0 to t = 2π.

> Find the area under the curve y = 2 + sin 3t from t = 0 to t = π/2.

> Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.

> Find the equation of the line tangent to the graph of y = tan t at t = π/4.

> Let f (p, q) = 1 - p(1 + q). Find ∂f/∂q and ∂f/∂p.

> The identity sin (s + t) = sin s cos t + cos s sin t was given in Section 8.2. Compute the partial derivative of each side with respect to t, and obtain an identity involving cos (s + t).

> If f (s, t) = t sin st, find ∂f/∂s and ∂f/∂t.

Question: Find ∂f/∂x and ∂f/∂y for