 Chapter 4.1: For Exercises 12, indicate all critical points on the given graphs....
 Chapter 4.2: For Exercises 12, indicate all critical points on the given graphs....
 Chapter 4.3: In Exercises 36, do the following: (a) Find f and f. (b) Find the c...
 Chapter 4.4: In Exercises 36, do the following: (a) Find f and f. (b) Find the c...
 Chapter 4.5: In Exercises 36, do the following: (a) Find f and f. (b) Find the c...
 Chapter 4.6: In Exercises 36, do the following: (a) Find f and f. (b) Find the c...
 Chapter 4.7: In Exercises 79, find the limits as x tends to + and , and then pro...
 Chapter 4.8: In Exercises 79, find the limits as x tends to + and , and then pro...
 Chapter 4.9: In Exercises 79, find the limits as x tends to + and , and then pro...
 Chapter 4.10: In Exercises 1013, find the global maximum and minimum for the func...
 Chapter 4.11: In Exercises 1013, find the global maximum and minimum for the func...
 Chapter 4.12: In Exercises 1013, find the global maximum and minimum for the func...
 Chapter 4.13: In Exercises 1013, find the global maximum and minimum for the func...
 Chapter 4.14: In Exercises 1416, find the exact global maximum and minimum values...
 Chapter 4.15: In Exercises 1416, find the exact global maximum and minimum values...
 Chapter 4.16: In Exercises 1416, find the exact global maximum and minimum values...
 Chapter 4.17: In Exercises 1723, use derivatives to identify local maxima and min...
 Chapter 4.18: In Exercises 1723, use derivatives to identify local maxima and min...
 Chapter 4.19: In Exercises 1723, use derivatives to identify local maxima and min...
 Chapter 4.20: In Exercises 1723, use derivatives to identify local maxima and min...
 Chapter 4.21: In Exercises 1723, use derivatives to identify local maxima and min...
 Chapter 4.22: In Exercises 1723, use derivatives to identify local maxima and min...
 Chapter 4.23: In Exercises 1723, use derivatives to identify local maxima and min...
 Chapter 4.24: Find the point where the following curve is steepest: y = 50 1+6e2t...
 Chapter 4.25: The graphs of the function f(x) = x/(x2 + a2) for a = 1, 2 , and 3,...
 Chapter 4.26: The graphs of the function f(x)=1eax for a = 1, 2, and 3, are shown...
 Chapter 4.27: (a) Find all critical points and all inflection points of the funct...
 Chapter 4.28: (a) For a a positive constant, find all critical points of f(x) = x...
 Chapter 4.29: If a and b are nonzero constants, find the domain and all critical ...
 Chapter 4.30: The average of two nonnegative numbers is 180. What is the largest ...
 Chapter 4.31: The product of three positive numbers is 192, and one of the number...
 Chapter 4.32: The difference between two numbers is 24. If both numbers are 100 o...
 Chapter 4.33: (a) Fixed costs are $3 million; variable costs are $0.4 million per...
 Chapter 4.34: A number x is increasing. When x = 10, the square of x is increasin...
 Chapter 4.35: The mass of a cube in grams is M = x3 + 0.1x4, where x is the lengt...
 Chapter 4.36: If is the angle between a line through the origin and the positive ...
 Chapter 4.37: In Exercises 3738, describe the motion of a particle moving accordi...
 Chapter 4.38: In Exercises 3738, describe the motion of a particle moving accordi...
 Chapter 4.39: Figure 4.115 is the graph of f , the derivative of a function f. At...
 Chapter 4.40: Figure 4.116 is a graph of f . For what values of x does f have a l...
 Chapter 4.41: On the graph of f in Figure 4.117, indicate the xvalues that are c...
 Chapter 4.42: Graph f given that: f (x)=0 at x = 2, f (x) < 0 for x < 2, f (x) > ...
 Chapter 4.43: A cubic polynomial with a local maximum at x = 1, a local minimum a...
 Chapter 4.44: A quartic polynomial whose graph is symmetric about the yaxis and ...
 Chapter 4.45: A function of the form y = axb ln x, where a and b are nonzero cons...
 Chapter 4.46: A function of the form y = A sin(Bx) + C with a maximum at (5, 2), ...
 Chapter 4.47: A function of the form y = axebx2 with a global maximum at (1, 2) a...
 Chapter 4.48: A closed rectangular box, with a square base x by x cm and height h...
 Chapter 4.49: A opentopped rectangular box, with a square base x by x cm and hei...
 Chapter 4.50: A closed cylinder with radius r cm and height h cm.
 Chapter 4.51: A cylinder open at one end with radius r cm and height h cm
 Chapter 4.52: In 5254, find the best possible bounds for the functions
 Chapter 4.53: In 5254, find the best possible bounds for the functions
 Chapter 4.54: In 5254, find the best possible bounds for the functions
 Chapter 4.55: Find the value(s) of m, if any, that give the global maximum and mi...
 Chapter 4.56: Find values of a and b so that the function y = axebx has a local m...
 Chapter 4.57: (a) Find all critical points of f(t) = at2ebt, assuming a and b are...
 Chapter 4.58: What effect does increasing the value of a have on the graph of f(x...
 Chapter 4.59: Sketch several members of the family y = x3 ax2 on the same axes. S...
 Chapter 4.60: Sketch several members of the family y = x3 ax2 on the same axes. S...
 Chapter 4.61: An object at a distance p from a thin glass lens produces an image ...
 Chapter 4.62: Any body radiates energy at various wavelengths. Figure 4.118 shows...
 Chapter 4.63: An electric current, I, in amps, is given by I = cos(wt) + 3 sin(wt...
 Chapter 4.64: The efficiency of a screw, E, is given by E = ( 2) + , > 0, where i...
 Chapter 4.65: A rectangle has one side on the xaxis and two corners on the top h...
 Chapter 4.66: The hypotenuse of a right triangle has one end at the origin and on...
 Chapter 4.67: Which point on the parabola y = x2 is nearest to (1, 0)? Find the c...
 Chapter 4.68: Find the coordinates of the point on the parabola y = x2 which is c...
 Chapter 4.69: The crosssection of a tunnel is a rectangle of height h surmounted...
 Chapter 4.70: A landscape architect plans to enclose a 3000 squarefoot rectangul...
 Chapter 4.71: A rectangular swimming pool is to be built with an area of 1800 squ...
 Chapter 4.72: A rectangular swimming pool is to be built with an area of 1800 squ...
 Chapter 4.73: A manufacturers cost of producing a product is given in Figure 4.12...
 Chapter 4.74: Using the cost and revenue graphs in Figure 4.120, sketch the follo...
 Chapter 4.75: A ship is steaming due north at 12 knots (1 knot = 1.85 kilometers/...
 Chapter 4.76: A polystyrene cup is in the shape of a frustum (the part of a cone ...
 Chapter 4.77: Suppose g(t) = (ln t)/t for t > 0. (a) Does g have either a global ...
 Chapter 4.78: For a > 0, the following line forms a triangle in the first quadran...
 Chapter 4.79: (a) Water is flowing at a constant rate (i.e., constant volume per ...
 Chapter 4.80: The vase in Figure 4.121 is filled with water at a constant rate (i...
 Chapter 4.81: A chemical storage tank is in the shape of an inverted cone with de...
 Chapter 4.82: In 8283, describe the form of the limit (0/0, /, 0, , 1, 00, 0, or ...
 Chapter 4.83: In 8283, describe the form of the limit (0/0, /, 0, , 1, 00, 0, or ...
 Chapter 4.84: In 8487, determine whether the limit exists, and where possible eva...
 Chapter 4.85: In 8487, determine whether the limit exists, and where possible eva...
 Chapter 4.86: In 8487, determine whether the limit exists, and where possible eva...
 Chapter 4.87: In 8487, determine whether the limit exists, and where possible eva...
 Chapter 4.88: The rate of change of a population depends on the current populatio...
 Chapter 4.89: A spherical cell is growing at a constant rate of 400 m3/day (1 m= ...
 Chapter 4.90: A raindrop is a perfect sphere with radius r cm and surface area S ...
 Chapter 4.91: A horizontal disk of radius a centered at the origin in the xyplan...
 Chapter 4.92: The depth of soot deposited from a smokestack is given by D = K(r +...
 Chapter 4.93: The mass of a circular oil slick of radius r is M = K (r ln(1 + r))...
 Chapter 4.94: Ice is being formed in the shape of a circular cylinder with inner ...
 Chapter 4.95: Sand falls from a hopper at a rate of 0.1 cubic meters per hour and...
 Chapter 4.96: (a) A hemispherical bowl of radius 10 cm contains water to a depth ...
 Chapter 4.97: A particle lies on a line perpendicular to a thin circular ring and...
 Chapter 4.98: A voltage, V volts, applied to a resistor of R ohms produces an ele...
 Chapter 4.99: A train is heading due west from St. Louis. At noon, a plane flying...
 Chapter 4.100: A fixed quantity of gas is allowed to expand at constant temperatur...
 Chapter 4.101: A fixed quantity of gas is allowed to expand at constant temperatur...
 Chapter 4.102: A population, P, in a restricted environment may grow with time, t,...
 Chapter 4.103: For positive a, consider the family of functions y = arctan x + a 1...
 Chapter 4.104: The function arcsinh x is the inverse function of sinh x. (a) Use a...
 Chapter 4.105: The function arccosh x, for x 0, is the inverse function of cosh x,...
 Chapter 4.106: Consider the family of functions f(x) = a + x a + x, x 0, for posit...
 Chapter 4.107: a) Use a computer algebra system to find the derivative of y = arct...
 Chapter 4.108: In 1696, the first calculus textbook was published by the Marquis d...
Solutions for Chapter Chapter 4: USING THE DERIVATIVE
Full solutions for Calculus: Single Variable  6th Edition
ISBN: 9780470888643
Solutions for Chapter Chapter 4: USING THE DERIVATIVE
Get Full SolutionsSince 108 problems in chapter Chapter 4: USING THE DERIVATIVE have been answered, more than 32292 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643. Chapter Chapter 4: USING THE DERIVATIVE includes 108 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6.

Angle of depression
The acute angle formed by the line of sight (downward) and the horizontal

Conic section (or conic)
A curve obtained by intersecting a doublenapped right circular cone with a plane

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Fivenumber summary
The minimum, first quartile, median, third quartile, and maximum of a data set.

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Graphical model
A visible representation of a numerical or algebraic model.

Magnitude of a real number
See Absolute value of a real number

Obtuse triangle
A triangle in which one angle is greater than 90°.

Partial fractions
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

Quotient rule of logarithms
logb a R S b = logb R  logb S, R > 0, S > 0

Radian measure
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Real number line
A horizontal line that represents the set of real numbers.

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Second quartile
See Quartile.

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Summation notation
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

Terminal side of an angle
See Angle.

Unit vector
Vector of length 1.

Venn diagram
A visualization of the relationships among events within a sample space.