Let ((x, y) = 5 - 2x + 4y - 3x2 - y2 . (A) Find the maximum value of ( (x, y) when x = 2. (B) Explain why the answer to part (A) is not the maximum value of the function ( (x, y).
> Find each indefinite integral and check the result by differentiating.
> Use the method of Lagrange multipliers.
> Use the method of Lagrange multipliers.
> Use the method of Lagrange multipliers. Minimize the product of two numbers if their difference must be 10.
> Use the method of Lagrange multipliers Find the maximum and minimum of ((x, y) = x2 - y2 subject to x2 + y2 = 25.
> use Theorem 1 to explain why no maxima or minima exist.
> Use the method of Lagrange multipliers.
> Use the method of Lagrange multipliers.
> find (′(0), ( ″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.
> find (′(0), ( ″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.
> find (′(0), ( ″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.
> Find each indefinite integral. Check by differentiating.
> find (′(0), ( ″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.
> A shipping box is to be reinforced with steel bands in all three directions, as shown in the figure. A total of 150 inches of steel tape is to be used, with 6 inches of waste because of a 2-inch overlap in each direction. Find the dimensions of the box w
> A rectangular box with no top and two intersecting partitions (see the figure) must hold a volume of 72 cubic inches. Find the dimensions that will require the least material.
> Repeat Problem 45, replacing the coordinates of B with B(6, 9) and the coordinates of C with C(9, 0). Data from Problem 45: A satellite TV station is to be located at P1x, y2 so that the sum of the squares of the distances from P to the three towns A, B
> A store sells two brands of laptop sleeves. The store pays $25 for each brand A sleeve and $30 for each brand B sleeve. A consulting firm has estimated the daily demand equations for these two competitive products to be x = 130 - 4p + q Demand equation
> The annual labor and automated equipment cost (in millions of dollars) for a company’s production of HDTVs is given by where x is the amount spent per year on labor and y is the amount spent per year on automated equipment (both in mi
> (A) Show that (0, 0) is a critical point of the function g(x, y) = exy2 + x2 y3 + 2, but that the second derivative test for local extrema fails. (B) Use cross sections, as in Example 2, to decide whether g has a local maximum, a local minimum, or a sad
> (A) Find the local extrema of the functions (B) Discuss the local extrema of the function K(x, y) = xn + yn , where n is a positive integer.
> Use Theorem 2 to find the local extrema.
> Use Theorem 2 to find the local extrema.
> Find each indefinite integral and check the result by differentiating.
> Use Theorem 2 to find the local extrema.
> Use Theorem 2 to find the local extrema.
> Use Theorem 2 to find the local extrema.
> Use Theorem 2 to find the local extrema.
> Use Theorem 2 to find the local extrema.
> Use Theorem 2 to find the local extrema.
> Use Theorem 2 to find the local extrema.
> Use Theorem 2 to find the local extrema.
> find (x(x, y)and (y(x, y), and explain, using Theorem 1, why ((x, y) has no local extrema.
> find (x(x, y)and (y(x, y), and explain, using Theorem 1, why ((x, y) has no local extrema.
> Find each indefinite integral. Check by differentiating.
> find (x(x, y)and (y(x, y), and explain, using Theorem 1, why ((x, y) has no local extrema.
> find (x(x, y)and (y(x, y), and explain, using Theorem 1, why ((x, y) has no local extrema.
> Find the indicated derivative.
> Find the indicated derivative.
> Find the indicated derivative.
> Find the indicated derivative.
> Poiseuille’s law states that the resistance R for blood flowing in a blood vessel varies directly as the length L of the vessel and inversely as the fourth power of its radius r. Stated as an equation, Find RL(4, 0.2) and Rr(4, 0.2), a
> Use this test in Problem to determine whether the indicated products are competitive, complementary, or neither. The monthly demand equations for the sale of tennis rackets and tennis balls in a sporting goods store are
> Use this test in Problem to determine whether the indicated products are competitive, complementary, or neither. The daily demand equations for the sale of brand A coffee and brand B coffee in a supermarket are x = ((p, q) = 200
> Find each indefinite integral and check the result by differentiating.
> The productivity of an automobile manufacturing company is given approximately by the function ((x, y = 50√xy = 50x0.5 y0.5 with the utilization of x units of labor and y units of capital. (A) Find (x(x, y) and (y(x, y). (B) If the company is now usin
> A company manufactures 10- and 3-speed bicycles. The weekly demand and cost functions are where $p is the price of a 10-speed bicycle, $q is the price of a 3-speed bicycle, x is the weekly demand for 10-speed bicycles, y is the weekly demand for 3-spee
> A company spends $x per week on online advertising and $y per week on TV advertising. Its weekly sales were found to be given by S(x, y) = 10x0.4y0.8 Find Sx(3,000, 2,000) and Sy(3,000, 2,000), and interpret the results.
> For ((x, y) = 2xy2 , find
> Let ((x, y) = ex + 2ey + 3xy2 + 1. (A) Use graphical approximation methods to find d (to three decimal places) such that ((1, d) is the minimum value of ((x, y) when x = 1. (B) Find (x(1, d) and (y(1, d).
> For G(x, y) = x2 ln y - 3x - 2y + 1 find all values of x and y such that Gx(x, y) = 0 and Gy(x, y) = 0 simultaneously.
> For C(x, y) = 2x2 + 2xy + 3y2 - 16x - 18y + 54 find all values of x and y such that Cx(x, y) = 0 and Cy(x, y) = 0 simultaneously.
> Find (xx(x, y),(xy (x, y), (yx(x, y), and (yy(x, y) for each function (.
> Find (xx(x, y),(xy (x, y), (yx(x, y), and (yy(x, y) for each function (.
> Find each indefinite integral. Check by differentiating.
> Find (xx(x, y),(xy (x, y), (yx(x, y), and (yy(x, y) for each function (.
> (A) Find an example of a function ((x, y) such that ∂(/∂x = 3 and ∂(/∂y = 2. (B) How many such functions are there? Explain.
> S(T, r) = 50(T – 40)(5 – r) gives an ice cream shop’s daily sale as a function of temperature T (in °F) and rain r (in inches). Find the indicated quantity (include the appropriate units) and explain what it means. Srt(90, 1)
> S(T, r) = 50(T – 40)(5 – r) gives an ice cream shop’s daily sale as a function of temperature T (in °F) and rain r (in inches). Find the indicated quantity (include the appropriate units) and explain what it means. ST(90, 1)
> S(T, r) = 50(T – 40)(5 – r) gives an ice cream shop’s daily sale as a function of temperature T (in °F) and rain r (in inches). Find the indicated quantity (include the appropriate units) and explain what it means. S(80, 0)
> Find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120. Cyy(3, -2)
> Find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120. Cyx(x, y)
> Find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120. Cyy(x, y)
> Find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120. Cy(3, -2)
> Find the indicated function or value if C(x, y) = 3x2 + 10xy - 8y2 + 4x - 15y - 120.
> Find each indefinite integral and check the result by differentiating.
> could the given matrix be the transition matrix of an absorbing Markov chain?
> Find the indicated second-order partial derivative for each function ((x, y).
> Find the indicated second-order partial derivative for each function ((x, y).
> Find the indicated second-order partial derivative for each function ((x, y).
> Find the indicated second-order partial derivative for each function ((x, y).
> Find the indicated second-order partial derivative for each function ((x, y).
> Find the indicated second-order partial derivative for each function ((x, y).
> M(x, y) = 68 + 0.3x - 0.8y gives the mileage (in mpg) of a new car as a function of tire pressure x (in psi) and speed (in mph). Find the indicated quantity (include the appropriate units) and explain what it means. My(32, 50)
> M(x, y) = 68 + 0.3x - 0.8y gives the mileage (in mpg) of a new car as a function of tire pressure x (in psi) and speed (in mph). Find the indicated quantity (include the appropriate units) and explain what it means. M(22, 50)
> M(x, y) = 68 + 0.3x - 0.8y gives the mileage (in mpg) of a new car as a function of tire pressure x (in psi) and speed (in mph). Find the indicated quantity (include the appropriate units) and explain what it means. M(22, 40)
> find the indicated value.
> Find each indefinite integral. Check by differentiating.
> find the indicated value.
> find the indicated value.
> find the indicated value.
> Find the indicated first-order partial derivative for each function z = ((x, y)
> Find the indicated first-order partial derivative for each function z = ((x, y)
> Find the indicated first-order partial derivative for each function z = ((x, y)
> Find the indicated first-order partial derivative for each function z = ((x, y)
> Find the indicated derivative.
> Find the indicated derivative.
> Find the indicated derivative.
> Find each indefinite integral and check the result by differentiating.
> Find the indicated derivative.
> find the indicated value of the function of two or three variables. The height of a right circular cylinder is 6 feet and the diameter is also 6 feet. Find the total surface area.?
> find the indicated value of the function of two or three variables. The length, width, and height of a rectangular box are 30 centimeters, 15 centimeters, and 10 centimeters, respectively. Find the volume.
> find the indicated value of the function of two or three variables. The height of a trapezoid is 4 meters and the lengths of its parallel sides are 25 meters and 32 meters. Find the area.
> The force F of attraction between two masses m1 and m2 at distance r is given by Newton’s law of universal gravitation where G is a constant. Evaluate F(50, 100, 20) and F(50, 100, 40).
> Under ideal conditions, if a person driving a car slam on the brakes and skids to a stop, the length of the skid marks (in feet) is given by the formula For k = 0.000 013 3, find L(2,000, 40) and L(3,000, 60).
> Poiseuille’s law states that the resistance R for blood flowing in a blood vessel varies directly as the length L of the vessel and inversely as the fourth power of its radius r. Stated as an equation, Find R(8, 1) and R(4, 0.2).
> The packaging department in a company has been asked to design a rectangular box with no top and a partition down the middle (see the figure). Let x, y, and z be the dimensions of the box (in inches). Ignore the thickness of the material from which the b
> The petroleum company in Problem 69 is taken over by another company that decides to double both the units of labor and the units of capital utilized in the production of petroleum. Use the Cobb–Douglas production function given in Problem 69 to find the
> A company manufactures 10- and 3-speed bicycles. The weekly demand and cost equations are p = 230 - 9x + y q = 130 + x - 4y C(x, y) = 200 + 80x + 30y where $p is the price of a 10-speed bicycle, $q is the price of a 3-speed bicycle, x is the weekly dema
> Find each indefinite integral. Check by differentiating.
> A company spends $x thousand per week on online advertising and $y thousand per week on TV advertising. Its weekly sales are found to be given by S(x, y) = 5x2 y3 Find S(3, 2) and S(2, 3)
