 4.1: For Exercises 12, indicate all critical points on the givengraphs. ...
 4.2: For Exercises 12, indicate all critical points on the givengraphs. ...
 4.3: In Exercises 36, do the following:(a) Find f and f.(b) Find the cri...
 4.4: In Exercises 36, do the following:(a) Find f and f.(b) Find the cri...
 4.5: In Exercises 36, do the following:(a) Find f and f.(b) Find the cri...
 4.6: In Exercises 36, do the following:(a) Find f and f.(b) Find the cri...
 4.7: In Exercises 79, find the limits as x tends to + and ,and then proc...
 4.8: In Exercises 79, find the limits as x tends to + and ,and then proc...
 4.9: In Exercises 79, find the limits as x tends to + and ,and then proc...
 4.10: In Exercises 1013, find the global maximum and minimumfor the funct...
 4.11: In Exercises 1013, find the global maximum and minimumfor the funct...
 4.12: In Exercises 1013, find the global maximum and minimumfor the funct...
 4.13: In Exercises 1013, find the global maximum and minimumfor the funct...
 4.14: In Exercises 1416, find the exact global maximum and minimumvalues ...
 4.15: In Exercises 1416, find the exact global maximum and minimumvalues ...
 4.16: In Exercises 1416, find the exact global maximum and minimumvalues ...
 4.17: In Exercises 1723, use derivatives to identify local maximaand mini...
 4.18: In Exercises 1723, use derivatives to identify local maximaand mini...
 4.19: In Exercises 1723, use derivatives to identify local maximaand mini...
 4.20: In Exercises 1723, use derivatives to identify local maximaand mini...
 4.21: In Exercises 1723, use derivatives to identify local maximaand mini...
 4.22: In Exercises 1723, use derivatives to identify local maximaand mini...
 4.23: In Exercises 1723, use derivatives to identify local maximaand mini...
 4.24: Find the point where the following curve is steepest:y = 501+6e2t f...
 4.25: The graphs of the function f(x) = x/(x2 + a2) fora = 1, 2 , and 3, ...
 4.26: The graphs of the function f(x)=1eax for a = 1, 2,and 3, are shown ...
 4.27: (a) Find all critical points and all inflection points of thefuncti...
 4.28: (a) For a a positive constant, find all critical points off(x) = x ...
 4.29: If a and b are nonzero constants, find the domain and allcritical p...
 4.30: The average of two nonnegative numbers is 180. What isthe largest p...
 4.31: The product of three positive numbers is 192, and one ofthe numbers...
 4.32: The difference between two numbers is 24. If both numbersare 100 or...
 4.33: (a) Fixed costs are $3 million; variable costs are $0.4million per ...
 4.34: A number x is increasing. When x = 10, the square of xis increasing...
 4.35: The mass of a cube in grams is M = x3 + 0.1x4, wherex is the length...
 4.36: If is the angle between a line through the origin and thepositive x...
 4.37: In Exercises 3738, describe the motion of a particle movingaccordin...
 4.38: In Exercises 3738, describe the motion of a particle movingaccordin...
 4.39: Figure 4.115 is the graph of f, the derivative of a functionf. At w...
 4.40: Figure 4.116 is a graph of f. For what values of x doesf have a loc...
 4.41: On the graph of f in Figure 4.117, indicate the xvaluesthat are cr...
 4.42: Graph f given that: f(x)=0 at x = 2, f(x) < 0 for x < 2,f(x) > 0 fo...
 4.43: In 4347, find formulas for the functionsA cubic polynomial with a l...
 4.44: In 4347, find formulas for the functionsA quartic polynomial whose ...
 4.45: In 4347, find formulas for the functionsA function of the form y = ...
 4.46: In 4347, find formulas for the functionsA function of the form y = ...
 4.47: In 4347, find formulas for the functions. A function of the form y ...
 4.48: In 4851, find the dimensions of the solid giving themaximum volume,...
 4.49: In 4851, find the dimensions of the solid giving themaximum volume,...
 4.50: In 4851, find the dimensions of the solid giving themaximum volume,...
 4.51: In 4851, find the dimensions of the solid giving themaximum volume,...
 4.52: In 5254, find the best possible bounds for the functions.ex sin x, ...
 4.53: In 5254, find the best possible bounds for the functions.x sin x, f...
 4.54: In 5254, find the best possible bounds for the functions.x3 6x2 + 9...
 4.55: Find the value(s) of m, if any, that give the global maximumand min...
 4.56: Find values of a and b so that the function y = axebxhas a local ma...
 4.57: (a) Find all critical points of f(t) = at2ebt, assuminga and b are ...
 4.58: What effect does increasing the value of a have on thegraph of f(x)...
 4.59: Sketch several members of the family y = x3 ax2on the same axes. Sh...
 4.60: A drug is injected into a patient at a rate given by r(t) =atebt ml...
 4.61: An object at a distance p from a thin glass lens producesan image a...
 4.62: Any body radiates energy at various wavelengths. Figure4.118 shows ...
 4.63: An electric current, I, in amps, is given byI = cos(wt) + 3 sin(wt)...
 4.64: The efficiency of a screw, E, is given byE = ( 2) + , > 0,where is ...
 4.65: A rectangle has one side on the xaxis and two cornerson the top ha...
 4.66: The hypotenuse of a right triangle has one end at the originand one...
 4.67: Which point on the parabola y = x2 is nearest to (1, 0)?Find the co...
 4.68: Find the coordinates of the point on the parabola y = x2which is cl...
 4.69: The crosssection of a tunnel is a rectangle of height hsurmounted ...
 4.70: A landscape architect plans to enclose a 3000 squarefootrectangula...
 4.71: A rectangular swimming pool is to be built with an areaof 1800 squa...
 4.72: (a) A cruise line offers a trip for $2000 per passenger. Ifat least...
 4.73: A manufacturers cost of producing a product is given inFigure 4.120...
 4.74: Using the cost and revenue graphs in Figure 4.120, sketchthe follow...
 4.75: A ship is steaming due north at 12 knots (1 knot = 1.85kilometers/h...
 4.76: A polystyrene cup is in the shape of a frustum (the partof a cone b...
 4.77: Suppose g(t) = (ln t)/t for t > 0.(a) Does g have either a global m...
 4.78: For a > 0, the following line forms a triangle in the firstquadrant...
 4.79: (a) Water is flowing at a constant rate (i.e., constant volumeper u...
 4.80: The vase in Figure 4.121 is filled with water at a constantrate (i....
 4.81: A chemical storage tank is in the shape of an invertedcone with dep...
 4.82: In 8283, describe the form of the limit (0/0,/, 0, , 1, 00, 0, or n...
 4.83: In 8283, describe the form of the limit (0/0,/, 0, , 1, 00, 0, or n...
 4.84: In 8487, determine whether the limit exists, andwhere possible eval...
 4.85: In 8487, determine whether the limit exists, andwhere possible eval...
 4.86: In 8487, determine whether the limit exists, andwhere possible eval...
 4.87: In 8487, determine whether the limit exists, andwhere possible eval...
 4.88: The rate of change of a population depends on the currentpopulation...
 4.89: A spherical cell is growing at a constant rate of400 m3/day (1 m= 1...
 4.90: A raindrop is a perfect sphere with radius r cm and surfacearea S c...
 4.91: A horizontal disk of radius a centered at the origin inthe xyplane...
 4.92: The depth of soot deposited from a smokestack is givenby D = K(r + ...
 4.93: The mass of a circular oil slick of radius r is M =K (r ln(1 + r)),...
 4.94: Ice is being formed in the shape of a circular cylinderwith inner r...
 4.95: Sand falls from a hopper at a rate of 0.1 cubic metersper hour and ...
 4.96: (a) A hemispherical bowl of radius 10 cm contains waterto a depth o...
 4.97: A particle lies on a line perpendicular to a thin circularring and ...
 4.98: A voltage, V volts, applied to a resistor of R ohms producesan elec...
 4.99: A train is heading due west from St. Louis. At noon, aplane flying ...
 4.100: 100101 involve Boyles Law, which states that fora fixed quantity of...
 4.101: 100101 involve Boyles Law, which states that fora fixed quantity of...
 4.102: A population, P, in a restricted environment may growwith time, t, ...
 4.103: For positive a, consider the family of functionsy = arctan x + a1 a...
 4.104: The function arcsinh x is the inverse function of sinh x.(a) Use a ...
 4.105: The function arccosh x, for x 0, is the inverse functionof cosh x, ...
 4.106: Consider the family of functionsf(x) =a + x a + x, x 0, for positiv...
 4.107: (a) Use a computer algebra system to find the derivativeofy = arcta...
 4.108: In 1696, the first calculus textbook was published by theMarquis de...
Solutions for Chapter 4: USING THE DERIVATIVE
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 4: USING THE DERIVATIVE
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Since 108 problems in chapter 4: USING THE DERIVATIVE have been answered, more than 43291 students have viewed full stepbystep solutions from this chapter. Chapter 4: USING THE DERIVATIVE includes 108 full stepbystep solutions. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This expansive textbook survival guide covers the following chapters and their solutions.

artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in threedimensional space and ordered triples of real numbers

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Compounded continuously
Interest compounded using the formula A = Pert

Demand curve
p = g(x), where x represents demand and p represents price

Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.

Extracting square roots
A method for solving equations in the form x 2 = k.

Factored form
The left side of u(v + w) = uv + uw.

Inverse function
The inverse relation of a onetoone function.

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

Lemniscate
A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

Nappe
See Right circular cone.

Partial sums
See Sequence of partial sums.

Polar form of a complex number
See Trigonometric form of a complex number.

Present value of an annuity T
he net amount of your money put into an annuity.

Resolving a vector
Finding the horizontal and vertical components of a vector.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n  12d4,

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Zero factor property
If ab = 0 , then either a = 0 or b = 0.