Problem 1RE: For Exercises 12, indicate all critical points on the given graphs. Which correspond to local... Problem 2RE: For Exercises 12, indicate all critical points on the given graphs. Which correspond to local... Problem 3RE: In Exercises 36, do the following: (a) Find f and f. (b) Find the critical points of f. (c) Find any... Problem 4RE: In Exercises 36, do the following: (a) Find f and f. (b) Find the critical points of f. (c) Find any... Problem 5RE: In Exercises 36, do the following: (a) Find f and f. (b) Find the critical points of f. (c) Find any... Problem 6RE: In Exercises 36, do the following: (a) Find f and f. (b) Find the critical points of f. (c) Find any... Problem 7RE: In Exercises 79, find the limits as x tends to + and , and then proceed as in Exercises 36. (That... Problem 8RE: In Exercises 79, find the limits as x tends to + and , and then proceed as in Exercises 36. (That... Problem 9RE: In Exercises 79, find the limits as x tends to + and , and then proceed as in Exercises 36. (That... Problem 10RE: Assume b gives the blood pressure of a patient following a dose a of a drug. We wish to find the... Problem 11RE: Assume D gives the density of an object at a distance L from one end of the object. We wish to find... Problem 12RE: In Exercises 1215, find the global maximum and minimum for the function on the closed interval.... Problem 13RE: In Exercises 1215, find the global maximum and minimum for the function on the closed interval.... Problem 14RE: In Exercises 1215, find the global maximum and minimum for the function on the closed interval.... Problem 15RE: In Exercises 1215, find the global maximum and minimum for the function on the closed interval.... Problem 16RE: In Exercises 1618, find the exact global maximum and minimum values of the function.... Problem 17RE: In Exercises 1618, find the exact global maximum and minimum values of the function. g(t)=1t3+1fort0 Problem 18RE: In Exercises 1618, find the exact global maximum and minimum values of the function. f(x)=1(x1)2+2 Problem 19RE: In Exercises 1924, use derivatives to identify local maxima and minima and points of inflection.... Problem 20RE: In Exercises 1924, use derivatives to identify local maxima and minima and points of inflection.... Problem 21RE: In Exercises 1924, use derivatives to identify local maxima and minima and points of inflection.... Problem 22RE: In Exercises 1924, use derivatives to identify local maxima and minima and points of inflection.... Problem 23RE: In Exercises 1924, use derivatives to identify local maxima and minima and points of inflection.... Problem 24RE: In Exercises 1924, use derivatives to identify local maxima and minima and points of inflection.... Problem 25RE: When you cough, your windpipe contracts. The speed, (r), with which you expel air depends on the... Problem 26RE: Find the point where the following curve is steepest: y=501+6e2tfort0. Problem 27RE: The graphs of the function f(x) = x(x2 + a2) for a = 1, 2, and 3, are shown in Figure 4.1. Without a... Problem 28RE: The graphs of the function f(x) = 1eax for a = 1, 2, and 3, are shown in Figure 4.2. Without a... Problem 29RE: (a) Find all critical points and all inflection points of the function f(x) = x4 2ax2 + b. Assume a... Problem 30RE: (a) For a a positive constant, find all critical points of f(x)=xax. (b) What value of a gives a... Problem 31RE: If a and b are nonzero constants, find the domain and all critical points of f(x)=ax2xb. Problem 32RE: The average of two nonnegative numbers is 180. What is the largest possible product of these two... Problem 33RE Problem 34RE: The difference between two numbers is 24. If both numbers are 100 or greater, what is the minimum... Problem 35RE: (a) Fixed costs are 3 million; variable costs are 0.4 million per item. Write a formula for total... Problem 36RE: A number x is increasing. When x = 10, the square of x is increasing at 5 units per second. How fast... Problem 37RE: The mass of a cube in grams is M = x3 + 0.1x4, where x is the length of one side in centimeters. If... Problem 38RE: If is the angle between a line through the origin and the positive x-axis, the area, in cm2, of... Problem 39RE: In Exercises 3940, describe the motion of a particle moving according to the parametric equations.... Problem 40RE Problem 41RE: Figure 4.3 is the graph of f, the derivative of a function f. At which of the points 0, x1, x2, x3,... Problem 42RE: Figure 4.4 is a graph of f. For what values of x does f have a local maximum? A local minimum?... Problem 43RE: On the graph of f in Figure 4.5, indicate the x-values that are critical points of the function f... Problem 44RE: Graph f given that: f(x) = 0 at x = 2, f(x) 0 for x 2, f(x) 0 for x 2, f(x) = 0 at x = 4, f(x) ... Problem 45RE: In Problems 4549, find formulas for the functions. A cubic polynomial with a local maximum at x = 1,... Problem 46RE: In Problems 4549, find formulas for the functions. A quartic polynomial whose graph is symmetric... Problem 47RE: In Problems 4549, find formulas for the functions. A function of the form y = axb ln x, where a and... Problem 48RE: In Problems 4549, find formulas for the functions. A function of the form y = A sin(Bx) + C with a... Problem 49RE: In Problems 4549, find formulas for the functions. A function of the form y=axebx2 with a global... Problem 50RE: In Problems 5053, find the dimensions of the solid giving the maximum volume, given that the surface... Problem 51RE: In Problems 5053, find the dimensions of the solid giving the maximum volume, given that the surface... Problem 52RE: In Problems 5053, find the dimensions of the solid giving the maximum volume, given that the surface... Problem 53RE: In Problems 5053, find the dimensions of the solid giving the maximum volume, given that the surface... Problem 54RE: In Problems 5456, find the best possible bounds for the functions. exsinx,forx0 Problem 55RE: In Problems 5456, find the best possible bounds for the functions. xsinx,for0x2 Problem 56RE: In Problems 5456, find the best possible bounds for the functions. x36x2+9x+5,for0x5 Problem 57RE: Find the value(s) of m, if any, that give the global maximum and minimum of P as a function of m... Problem 58RE Problem 59RE: (a) Find all critical points of f(t)=at2ebt, assuming a and b are nonzero constants. (b) Find values... Problem 60RE: What effect does increasing the value of a have on the graph of f(x) = x2 +2ax? Consider roots,... Problem 61RE: Sketch several members of the family y = x3 ax2 on the same axes. Show that the critical points lie... Problem 62RE: A drug is injected into a patient at a rate given by r(t) = atebt ml/sec, where t is in seconds... Problem 63RE: An object at a distance p froma thin glass lens produces an image at a distance q from the lens,... Problem 64RE: Any body radiates energy at various wavelengths. Figure 4.6 shows the intensity of the radiation of... Problem 65RE: An electric current, I, in amps, is given by I=cos(wt)+3sin(wt), where w 0 is a constant. What are... Problem 66RE: The efficiency of a screw, E, is given by E=(2)+,0, where is the angle of pitch of the thread and ... Problem 67RE: A rectangle has one side on the x-axis and two corners on the top half of the circle of radius 1... Problem 68RE: The hypotenuse of a right triangle has one end at the origin and one end on the curve y = x2e3x,... Problem 69RE: Which point on the parabola y = x2 is nearest to (1, 0)? Find the coordinates to two decimals.... Problem 70RE: Find the coordinates of the point on the parabola y = x2 which is closest to the point (3,0). Problem 71RE: The cross-section of a tunnel is a rectangle of height surmounted by a semicircular roof section of... Problem 72RE: A landscape architect plans to enclose a 3000 square-foot rectangular region in a botanical garden.... Problem 73RE: A rectangular swimming pool is to be built with an area of 1800 square feet. The owner wants... Problem 74RE: (a) A cruise line offers a trip for 2000 per passenger. If at least 100 passengers sign up, the... Problem 75RE: A manufacturers cost of producing a product is given in Figure 4.8. The manufacturer can sell the... Problem 76RE: Using the cost and revenue graphs in Figure 4.8, sketch the following functions. Label the points q1... Problem 77RE: A ship is steaming due north at 12 knots (1 knot = 1.85 kilometers/hour) and sights a large tanker 3... Problem 78RE: A polystyrene cup is in the shape of a frustum (the part of a cone between two parallel planes... Problem 79RE: Suppose g(t) = (ln t)t for t 0. (a) Does g have either a global maximum or a global minimum on 0 t... Problem 80RE: For a 0, the following line forms a triangle in the first quadrant with the x- and y-axes: a(a2 +... Problem 81RE: (a) Water is flowing at a constant rate (i.e., constant volume per unit time) into a cylindrical... Problem 82RE: The vase in Figure 4.9 is filled with water at a constant rate (i.e., constant volume per unit... Problem 83RE Problem 84RE: In Problems 8485, describe the form of the limit (00, , 0, , 1, 00, 0, or none of these). Does... Problem 85RE: In Problems 8485, describe the form of the limit (00, , 0, , 1, 00, 0, or none of these). Does... Problem 86RE: In Problems 8485, describe the form of the limit (00, , 0, , 1, 00, 0, or none of these). Does... Problem 87RE: In Problems 8689, determine whether the limit exists, and where possible evaluate it.... Problem 88RE: In Problems 8689, determine whether the limit exists, and where possible evaluate it.... Problem 89RE: In Problems 8689, determine whether the limit exists, and where possible evaluate it.... Problem 90RE: The rate of change of a population depends on the current population, P, and is given by... Problem 91RE: A spherical cell is growing at a constant rate of 400 m3day (1 m= 106 m). At what rate is its radius... Problem 92RE: A raindrop is a perfect sphere with radius r cm and surface area S cm2. Condensation accumulates on... Problem 93RE: A horizontal disk of radius a centered at the origin in the xy-plane is rotating about a vertical... Problem 94RE: The depth of soot deposited from a smokestack is given by D = K(r + 1)er, where r is the distance... Problem 95RE Problem 96RE: Ice is being formed in the shape of a circular cylinder with inner radius 1 cm and height 3 cm. The... Problem 97RE: Sand falls from a hopper at a rate of 0.1 cubic meters per hour and forms a conical pile beneath. If... Problem 98RE: (a) Ahemispherical bowl of radius 10 cmcontains water to a depth of cm. Find the radius of the... Problem 99RE: A particle lies on a line perpendicular to a thin circular ring and through its center. The radius... Problem 100RE: A voltage, V volts, applied to a resistor of R ohms produces an electric current of I amps where V =... Problem 101RE: A train is heading due west from St. Louis. At noon, a plane flying horizontally due north at a... Problem 102RE: Problems 102103 involve Boyles Law, which states that for a fixed quantity of gas at a constant... Problem 103RE: A certain quantity of gas occupies 10 cm3 at a pressure of 2 atmospheres. The pressure is increased,... 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