 4.5.1: A positive number x and its reciprocal are added together.The small...
 4.5.2: Two nonnegative numbers, x and y, have a sum equal to10. The larges...
 4.5.3: A rectangle in the xyplane has one corner at the origin, anadjacen...
 4.5.4: An open box is to be made from a 20inch by 32inch pieceof cardboa...
 4.5.5: A rectangular plot of land is to be fenced in using two kindsof fen...
 4.5.6: A rectangle is to be inscribed in a right triangle having sidesof l...
 4.5.7: Solve the problem in Exercise 6 assuming the rectangle ispositioned...
 4.5.8: A rectangle has its two lower corners on the xaxis and itstwo uppe...
 4.5.9: Find the dimensions of the rectangle with maximum areathat can be i...
 4.5.10: Find the point P in the first quadrant on the curve y = x2such that...
 4.5.11: A rectangular area of 3200 ft2 is to be fenced off. Twoopposite sid...
 4.5.12: Show that among all rectangles with perimeter p, the squarehas the ...
 4.5.13: Show that among all rectangles with area A, the square hasthe minim...
 4.5.14: A wire of length 12 in can be bent into a circle, bent into asquare...
 4.5.15: A rectangle R in the plane has corners at (8, 12), anda 100 by 100 ...
 4.5.16: Solve the problem in Exercise 15 if S is a 16 by 16 square.
 4.5.17: Solve the problem in Exercise 15 if S is positioned with itslower l...
 4.5.18: A rectangular page is to contain 42 square inches of printablearea....
 4.5.19: A box with a square base is taller than it is wide. In orderto send...
 4.5.20: A box with a square base is wider than it is tall. In order tosend ...
 4.5.21: An open box is to be made from a 3 ft by 8 ft rectangularpiece of s...
 4.5.22: A closed rectangular container with a square base is to havea volum...
 4.5.23: A closed rectangular container with a square base is to havea volum...
 4.5.24: A container with square base, vertical sides, and open top isto be ...
 4.5.25: A rectangular container with two square sides and an opentop is to ...
 4.5.26: A church window consisting of a rectangle topped by a semicircleis ...
 4.5.27: Find the dimensions of the right circular cylinder of largestvolume...
 4.5.28: Find the dimensions of the right circular cylinder of greatestsurfa...
 4.5.29: A closed, cylindrical can is to have a volume of V cubicunits. Show...
 4.5.30: A closed cylindrical can is to have a surface area of S squareunits...
 4.5.31: A cylindrical can, open at the top, is to hold 500 cm3 ofliquid. Fi...
 4.5.32: A soup can in the shape of a right circular cylinder of radiusr and...
 4.5.33: A boxshaped wire frame consists of two identical wiresquares whose...
 4.5.34: Suppose that the sum of the surface areas of a sphere and acube is ...
 4.5.35: Find the height and radius of the cone of slant height Lwhose volum...
 4.5.36: A cone is made from a circular sheet of radius R by cuttingout a se...
 4.5.37: A coneshaped paper drinking cup is to hold 100 cm3 of water.Find t...
 4.5.38: Find the dimensions of the isosceles triangle of least areathat can...
 4.5.39: Find the height and radius of the right circular cone withleast vol...
 4.5.40: A commercial cattle ranch currently allows 20 steers peracre of gra...
 4.5.41: A company mines lowgrade nickel ore. If the companymines x tons of...
 4.5.42: A fertilizer producer finds that it can sell its product at aprice ...
 4.5.43: (a) A chemical manufacturer sells sulfuric acid in bulk at aprice o...
 4.5.44: A firm determines that x units of its product can be solddaily at p...
 4.5.45: In a certain chemical manufacturing process, the dailyweight y of d...
 4.5.46: An independent truck driver charges a client $15 for eachhour of dr...
 4.5.47: A trapezoid is inscribed in a semicircle of radius 2 so thatone sid...
 4.5.48: A drainage channel is to be made so that its cross sectionis a trap...
 4.5.49: A lamp is suspended above the center of a round table of radiusr. H...
 4.5.50: A plank is used to reach over a fence 8 ft high to support awall th...
 4.5.51: Two particles, A and B, are in motion in the xyplane.Their coordin...
 4.5.52: Follow the directions of Exercise 51, with xA = t,yA = t 2,xB = 2t,...
 4.5.53: Find the coordinates of the point P on the curvey = 1x2 (x > 0)wher...
 4.5.54: Find the xcoordinate of the point P on the parabolay = 1 x2 (0 < x...
 4.5.55: Where on the curve y =1 + x21 does the tangent linehave the greates...
 4.5.56: Suppose that the number of bacteria in a culture at time t isgiven ...
 4.5.57: The shoreline of Circle Lake is a circle with diameter 2 mi.Nancys ...
 4.5.58: A man is floating in a rowboat 1 mile from the (straight)shoreline ...
 4.5.59: A pipe of negligible diameter is to be carried horizontallyaround a...
 4.5.60: A concrete barrier whose cross section is an isosceles triangleruns...
 4.5.61: Suppose that the intensity of a point light source is directlypropo...
 4.5.62: Given points A(2, 1) and B(5, 4), find the point P in theinterval [...
 4.5.63: The lower edge of a painting, 10 ft in height, is 2 ft abovean obse...
 4.5.64: Fermats principle (biography on p. 275) in optics statesthat light ...
 4.5.65: Fermats principle (Exercise 64) also explains why lightrays traveli...
 4.5.66: A farmer wants to walk at a constant rate from her barnto a straigh...
 4.5.67: If an unknown physical quantity x is measured n times,the measureme...
 4.5.68: Prove: If f(x) 0 on an interval and if f(x) has a maximumvalue on t...
 4.5.69: Writing Discuss the importance of finding intervals of possiblevalu...
Solutions for Chapter 4.5: APPLIED MAXIMUM AND MIMIMUM PROBLEMS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 4.5: APPLIED MAXIMUM AND MIMIMUM PROBLEMS
Get Full SolutionsSince 69 problems in chapter 4.5: APPLIED MAXIMUM AND MIMIMUM PROBLEMS have been answered, more than 40309 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.5: APPLIED MAXIMUM AND MIMIMUM PROBLEMS includes 69 full stepbystep solutions. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691.

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Amplitude
See Sinusoid.

Coefficient
The real number multiplied by the variable(s) in a polynomial term

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

Directed line segment
See Arrow.

Halflife
The amount of time required for half of a radioactive substance to decay.

Horizontal shrink or stretch
See Shrink, stretch.

Initial point
See Arrow.

Law of sines
sin A a = sin B b = sin C c

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Logarithm
An expression of the form logb x (see Logarithmic function)

Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Vertical stretch or shrink
See Stretch, Shrink.

Whole numbers
The numbers 0, 1, 2, 3, ... .