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variables is called a complete integral (or) complete solution. variables. The length of its base is twice the width. Then, determine the x- coordinates of all relative maxima and minima. Find the intervals on which f is increasing or decreasing, find the local maximum and minimum values of f(x), and the intervals of concavity and inflexion points. R(x) = -x^2 + 8x, C(x) = 3x + 4 A. Graph both functions. With these equations the function represents physical quantities and the derivatives their rate of change. f(x) has 4 critical points. (a) Find the local maxima of A. Find the relative extrema. The fruit tree yield per tree in an orchard containing 40 trees is 76 pounds per tree each year. Find all local maximum, local minimum, and saddle points of f (x,y) = xy - 2x - 2y - x^2 - y^2. The materials for the base of the crate cost $2 per square foot. To reorder, there is a fixed cost of$20 per shipment plus $10 for each pool table. 5. By Find the slope of the line through P such that the triangle bounded by this line and the axes in the first quadrant has minimal area. Currently the hotel is filled. 10) 2xy dy dx +y2 −2x = 0 Exercise 3. Use a graph or level curves or both to find the local maximum and minimum values and saddle points of the function. solution. Here, P= x (y2-z2) ,Q= y (z2-x2) , R= z (x2-y2) Use Lagrangian multipliers x,y,z, We get the ratio in (1) logx +logy+logz=log b. How long does it take to reach... Liana has 54 yards of fencing to enclose a rectangular region. giving your answer in the form y = f(x) (Total for question 3 is 12 marks) (3) (5) (4) (x + 1)(2x −1) dy dx = y(3x − 3) 4 Find the general solution to the differential equation (Total for question 4 is 6 marks) dy dx = xysinx 5 Find the general solution to the differential equation (Total for question 5 … Find the x-coordinate on the graph of the equation y = x^3 that is closest to the point (3, 0). Its length is 30 yards longer than its width. Then use the Second Derivative Test to determine whether they are local minima, local maxima, or saddle points (or state that the test fails). For each$25 increase in rent, however, an average of one unit becomes vacant. 1. f(x) = 2x^2 + 20x +53 2. f(x) = frac{6x}{x^2 + 1} 3. f(x) = sqrt[3]{x + 1}. A. z=4x+5y 2x+y Farmers can get 8 per bushel for their potatoes on July 1, and after that, the price drops by 8 cents per bushel per day. For each 1 dollar increase in the daily rate, 5 fewer cars are rented. Use the 2nd derivative test to find the extremer of on the interval 0,2\pi, f(x) = 2cosx + sin 2x. What is the shortest ladder that can extend from the ground to the house without touching the fence? a. Find the dimensions of the largest package that can be sent. Which one of the following properties does the function f(x,y) = x^3 + 3xy - 9x - 3y + 23 have? Find the dimensions of the triangle and square that produce a minimum total area. Answer. The Hotel Bellville has 400 rooms. The electric field at a point on its axis a distance x from its center is given as: E=\frac{1}... Farmer Brown wants to fence in a rectangular plot in a large field, using a straight rock wall that is already there as the north boundary. Consider the differential equation y" + ay' + By = t+e*. We advise you to convert it to a fully qualified order and we will try to help you. The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. 2x+y One piece is used to tom, a square, and the remaining piece is used to form a circle. Determine the maximum possible area of the rectangle. φ(xy)=φ(x)φ(y)  ∀x,y∈G Find the two numbers whose product is as large as possible. Find the absolute maximum and minimum, if either exists, for f(x) = 16x^3 - 3x^4. Every $2 decrease in price attracts an additional 60 customers. Waste Management Company wants to construct a dumpster in the shape of a rectangular solid with no top whose length is four times its width. Check the condition of integrability & solve Find any critical numbers for the function f(x) = x^{19/9} - x^{10/9} and then use the second derivative test to decide whether the critical numbers lead to relative maxima or relative minima. When the rent is$1,460 per month, all units are occupied. A function and values of x so that f^{-1}(x) = 0 are given. If two light sources... Let C(x) be the cost to produce x widgets, and let R(x) be the revenue. Find the points on the ellipse 4 x 2 + y 2 = 16 that are farthest away from the point ( 3 , 0 ) . A drinking cup is made in the shape of a right circular cylinder. 1. y x x x. a. Determine the time when the concentration is highest. The open intervals where the function is increasing, c. The open intervals where it is decreasing. f (x) =2x \ 3 - 15... For f (x) = 4 x^3 - x^2 - 24 x + 5, find: 1) critical x-values. Show Answer. The length (in centimeters) of a typical Pacific halibut t years old is approximately f(t) = 220(1- 0.966e-0.24t). There are 480 feet of fencing av... As x ranges over all real values, what is the minimum value of f(x)= |x - 123| + |x - 456| + |x - 789|? f(x) = x + {4 \over x}. 1. Use the Second Derivative Test if applicable. If yes, try our quiz and see if you know everything about differential equations. A rectangle is inscribed in a semi-circle of diameter d as shown below. We want to find the length of the shortest ladder that will reach from the ground over the fence to the w... A function and values of x so that f 0(x) = 0 are given. Find the numbers if their product is a maximum. A fence must be built to enclose a rectangular area of 5000 ft/square. which passes through the, Find the integral surface of the differential equation (y+zq)^2 = z^2 (1+p^2+q^2) can be written as. If the cardboard is 24 inches long and 15 inches... Find and identify (max/min) all relative extrema: f(x) =2x^3 + 3x^2 -12x. This equation of the form        f (x, p, q) =0 . Test your understanding with practice problems and step-by-step solutions. Since he has owned the car for several ye... A physical fitness room consists of a rectangular region with a semicircle at each end. Suppose the total revenue function or a product is given by R(x) = 32x - 0.01x^2 (a) How many units will maximize the total revenue? The material for the top costs 10 centavos per square cm, while the material for the sides... Chris makes an open-topped box from a 30-cm by 30-cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. The sum of a number and two times another number is 32. The fuel consumption c of Micheal's car ( measured in gallons per hour ) is a function of speed ( or velocity ) v of the car ( measured in miles per hour). At a price of $26 per ticket, attendance averages 40,000 people per game. A farmer wants to construct a fence around a rectangular field. Replace D by m and D’ by 1. You are assigned the task of designing a cylindrical can that holds a volume of 1 cubic foot of liquid. 5 b. If the demand for x gimcracks at price p is determined by the equation 3x + 5p = 1500, (a) What production will maximize revenue? The function f has continuous second derivatives and a critical point at (7, 3). Copyright © 2018-2021 BrainKart.com; All Rights Reserved. margins at the bottom and sides and a 2-in. A box with a square base and open top is to have a volume of 90000 cubic inches. I'm having a hard time factoring the cubic polynomial. Professor Tim was at the beach with his dog Elvis. Let A(x) = x sqrt{x + 4}. List the points where they occur. will yield a gutter that holds the most water? Find all critical points of f(x) = 5x^7 + 35x^6 - 49x^5 and classify each as a relative minimum, relative maximum, or neither one. The height (in feet) attained by a rocket t seconds into flight is giving by the function h(t)= (-1/3t)^3 + 16t^2 + 33t + 10. D by m He drives a golf ball with an initial velocity v_0= \left \langle 0, 20, 49 \right \rangle m/s. f(x) = x^3 - 3/2 x^2, [ -5, 2]. for any assignment or question with DETAILED EXPLANATIONS! What is the Difference Between Research Proposal and Research Report? Find the number of automobiles that must be produced to minim... A small blood vessel of radius 2mm branches off at an angle from a larger blood vessel of radius 4mm. A. y(k) = 4 – 5/k; B. y(k) = 20 + 5k It costs$10 to store one pool table for a year. You are to design a right cylindrical tank that has a volume, 32 ft^2 . > a) $20 b)$2.50 c) $50.00 d)$40 e) None of these, Find the absolute maximum and absolute minimum values of the function on the given interval. Find all critical points of f(x). What dimensions will yield a box of maximum volume? How many kinds of differential equations were listed by Newton? what should its dimensions be? A firm can produce 100 units per week. What dimensions will give the largest printed area? 2.From the PDE by Two opposite sides will use heavy-duty fencing selling for \$3/ft, while the remaining two sides will use standard fencing s... Find the dimensions of a rectangle with maximum area that can be inscribed in a circle of a radius of 10. that occur in the functional relation between the dependent and independent A handball court is to be surrounded by plastic stripping 30 m long.