 4.5.1: Two numbers add to 5. What is the largest possible value of their p...
 4.5.2: Find two numbers adding to 20 such that the sum of their squares is...
 4.5.3: The difference of two numbers is 1. What is the smallest possible v...
 4.5.4: For each quadratic function, state whether it would make sense to l...
 4.5.5: Among all rectangles having a perimeter of 25 m, find the dimension...
 4.5.6: What is the largest possible area for a rectangle with a perimeter ...
 4.5.7: What is the largest possible area for a right triangle in which the...
 4.5.8: The perimeter of a rectangle is 12 m. Find the dimensions for which...
 4.5.9: Two numbers add to 6. (a) Let T denote the sum of the squares of th...
 4.5.10: Suppose that the height of an object shot straight up is given by h...
 4.5.11: A baseball is thrown straight up, and its height as a function of t...
 4.5.12: Find the point on the curve y that is nearest to the point (3, 0).
 4.5.13: Which point on the curve y 1 is closest to the point (4, 1)? What i...
 4.5.14: Find the coordinates of the point on the line y 3x 1 closest to (4,...
 4.5.15: (a) What number exceeds its square by the greatest amount? (b) What...
 4.5.16: Suppose that you have 1800 m of fencing with which to build three a...
 4.5.17: Five hundred feet of fencing is available for a rectangular pasture...
 4.5.18: Let A 3x2 4x 5 and B x2 4x 1. Find the minimum value of A B. 19.
 4.5.19: Let R 0.4x2 10x 5 and C 0.5x2 2x 101. For which value of x is R C a...
 4.5.20: Suppose that the revenue generated by selling x units of a certain ...
 4.5.21: Suppose that the function p 30 relates the selling price p of an it...
 4.5.22: The action of sunlight on automobile exhaust produces air pollutant...
 4.5.23: (a) Find the smallest possible value of the quantity x2 y2 under th...
 4.5.24: (a) Find the coordinates of the vertex of the parabola y 2x2 4x 7. ...
 4.5.25: (a) Using a graphing utility, graph the two functions y x4 2 and y ...
 4.5.26: Through a type of chemical reaction known as autocatalysis, the hum...
 4.5.27: (a) Let x y 15. Find the minimum value of the quantity x2 y2 . (b) ...
 4.5.28: Suppose that A, B, and C are positive constants and that x y C. Sho...
 4.5.29: The following figure shows a square inscribed within a unit square....
 4.5.30: (a) Show that the coordinates of the point on the line y mx b that ...
 4.5.31: The point P lies in the first quadrant on the graph of the line y 7...
 4.5.32: Show that the largest possible area for the shaded rectangle shown ...
 4.5.33: Show that the maximum possible area for a rectangle inscribed in a ...
 4.5.34: An athletic field with a perimeter of mile consists of a rectangle ...
 4.5.35: A rancher who wishes to fence off a rectangular area finds that the...
 4.5.36: Let f(x) (x a) 2 (x b) 2 (x c) 2 , where a, b, and c are constants....
 4.5.37: Let y a1(x x1) 2 a2(x x2) 2 , where a1, a2, x1, and x2 are all cons...
 4.5.38: Among all rectangles with a given perimeter P, find the dimensions ...
 4.5.39: By analyzing sales figures, the economist for a stereo manufacturer...
 4.5.40: Let f(x) x2 px q, and suppose that the minimum value of this functi...
 4.5.41: Among all possible inputs for the function f(t) t 4 6t 2 6, which o...
 4.5.42: Let f(x) x 3 and g(x) x2 4x 1. (a) Find the minimum value of g f. (...
 4.5.43: This exercise completes a detail mentioned in Example 4. In that ex...
 4.5.44: Let f(x) (x 1)2 4. (a) Sketch the graph of the function f and note ...
 4.5.45: A piece of wire 16 in. long is to be cut into two pieces. Let x den...
 4.5.46: A 30in. piece of string is to be cut into two pieces. The first pi...
 4.5.47: Exercises 4752 are maximumminimum problems in which the function t...
 4.5.48: Exercises 4752 are maximumminimum problems in which the function t...
 4.5.49: Exercises 4752 are maximumminimum problems in which the function t...
 4.5.50: Exercises 4752 are maximumminimum problems in which the function t...
 4.5.51: Exercises 4752 are maximumminimum problems in which the function t...
 4.5.52: Exercises 4752 are maximumminimum problems in which the function t...
 4.5.53: (a) Use a graphing utility to graph the parabolas y x2 2x, y x2 2x,...
 4.5.54: (a) Graph the four parabolas y x2 2kx 1 corresponding to k 2, 3, 0....
 4.5.55: The figure shows a rectangle inscribed in a given triangle of base ...
 4.5.56: A Norman window is in the shape of a rectangle surmounted by a semi...
 4.5.57: A triangle is inscribed in a semicircle of diameter 2R, as shown in...
 4.5.58: (a) Complete the following table. Which xy pair in the table yield...
 4.5.59: What is the smallest possible value for the sum of a positive numbe...
 4.5.60: Suppose that a and b are positive numbers whose sum is 1. (a) Find ...
Solutions for Chapter 4.5: MAXIMUM AND MINIMUM PROBLEMS
Full solutions for Precalculus: With Unit Circle Trigonometry (with Interactive Video Skillbuilder CDROM) (Available 2010 Titles Enhanced Web Assign)  4th Edition
ISBN: 9780534402303
Solutions for Chapter 4.5: MAXIMUM AND MINIMUM PROBLEMS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 60 problems in chapter 4.5: MAXIMUM AND MINIMUM PROBLEMS have been answered, more than 25544 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus: With Unit Circle Trigonometry (with Interactive Video Skillbuilder CDROM) (Available 2010 Titles Enhanced Web Assign), edition: 4. Precalculus: With Unit Circle Trigonometry (with Interactive Video Skillbuilder CDROM) (Available 2010 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780534402303. Chapter 4.5: MAXIMUM AND MINIMUM PROBLEMS includes 60 full stepbystep solutions.

Compound interest
Interest that becomes part of the investment

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

Equivalent vectors
Vectors with the same magnitude and direction.

Explanatory variable
A variable that affects a response variable.

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

Horizontal component
See Component form of a vector.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Index of summation
See Summation notation.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Multiplication property of inequality
If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

Negative numbers
Real numbers shown to the left of the origin on a number line.

Real number
Any number that can be written as a decimal.

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Rigid transformation
A transformation that leaves the basic shape of a graph unchanged.

Slope
Ratio change in y/change in x

Transpose of a matrix
The matrix AT obtained by interchanging the rows and columns of A.

Unit vector
Vector of length 1.

xintercept
A point that lies on both the graph and the xaxis,.

Xmax
The xvalue of the right side of the viewing window,.