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mathematics
college mathematics for business
Questions and Answers of
College Mathematics For Business
In Problem find the indicated extremum of each function on the given interval.Absolute maximum value on (0, ∞) forf(x) = ln (xe-x)
The ceiling supports in a new discount department store are 12 feet apart. Lights are to be hung from these supports by chains in the shape of a “Y.” If the lights are 10 feet below the ceiling,
In Problem find the absolute maximum and minimum, if either exists, for each function on the indicated intervals.f(x) = x3 - 6x2 + 9x - 6(A) [-1, 5] (B) [-1, 3] (C) [2, 5]
The table gives the total daily cost y (in dollars) of producing x dozen chocolate chip cookies at various production levels.(A) Enter the data into a graphing calculator and find a quadratic
In Problem find the absolute maximum and minimum, if either exists, for each function on the indicated intervals.f(x) = (x - 1) (x - 5)3 + 1(A) [0, 3] (B) [1, 7] (C) [3, 6]
A chain of appliance stores uses TV ads to promote its HDTV sales. Analyzing past records produced the data in the following table, where x is the number of ads placed monthly and y is the number of
In Problem find the absolute maximum and minimum, if either exists, for each function on the indicated intervals.f(x) = x4 - 4x3 + 5(A) [-1, 2] (B) [0, 4] (C) [-1, 1]
If t days after a treatment the bacteria count per cubic centimeter in a body of water is given byC(t) = 20t2 - 120t + 800 0 ≤ t ≤ 9then in how many days will the count be a minimum?
In a new suburb, the number of registered voters is estimated to beN(t) = 10 + 6t2 - t3 0 ≤ t ≤ 5where t is time in years and N is in thousands. When will the rate of increase of N(t) be at
In Problem describe the graph of f at the given point relative to the existence of a local maximum or minimum with one of the following phrases: “Local maximum,” “Local minimum,”
In Problem describe the graph of f at the given point relative to the existence of a local maximum or minimum with one of the following phrases: “Local maximum,” “Local minimum,”
In Problem describe the graph of f at the given point relative to the existence of a local maximum or minimum with one of the following phrases: “Local maximum,” “Local minimum,”
In Problem describe the graph of f at the given point relative to the existence of a local maximum or minimum with one of the following phrases: “Local maximum,” “Local minimum,”
In Problem describe the graph of f at the given point relative to the existence of a local maximum or minimum with one of the following phrases: “Local maximum,” “Local minimum,”
In Problem describe the graph of f at the given point relative to the existence of a local maximum or minimum with one of the following phrases: “Local maximum,” “Local minimum,”
In Problem describe the graph of f at the given point relative to the existence of a local maximum or minimum with one of the following phrases: “Local maximum,” “Local minimum,”
In Problem describe the graph of f at the given point relative to the existence of a local maximum or minimum with one of the following phrases: “Local maximum,” “Local minimum,”
Find two positive numbers whose product is 19 and whose sum is a minimum.
Problem refer to the graph of y = f(x) shown here. Find the absolute minimum and the absolute maximum over the indicated interval.[0, 9] f(x) 15 10 10
In Problem find the domain and intercepts. f(x) = In(x + 2)
In Problem match the indicated conditions with one of the graphs (A)–(D) shown in the figure.f′(x) > 0 and f″(x) > 0 on (a, b) f(x) f(x) f(x) fr) to to a a b. a a b. (A) (B) (C) (D)
Problem refer to the following graph of y = f(x):Identify the x coordinates of the points where f′(x) = 0. fx) a d e
Problem refer to the graph of y = f(x) shown here. Find the absolute minimum and the absolute maximum over the indicated interval.[1, 10] f(x) 15 10 10
In Problem find the domain and intercepts. 5 + x f(x) 4 - x ||
Use the graph of y = f(x) to identify(A) The local extrema of f(x).(B) The inflection points of f(x).(C) The numbers u for which f′(u) is a local extremum of f′(x). -5 f(x) Figure for 12 X
Problem refer to the following graph of y = f(x):Identify the intervals on which f′(x) > 0. fx) a d e
Find two positive numbers whose product is 13 and whose sum is a minimum.
Problem refer to the graph of y = f(x) shown here. Find the absolute minimum and the absolute maximum over the indicated interval.[2, 10] f(x) 15 10 10
Problem refer to the following graph of y = f(x):Identify the intervals on which f′(x) < 0. fx) a d e
Use the graph of y = f(x) to identify(A) The local extrema of f(x).(B) The inflection points of f(x).(C) The numbers u for which f′(u) is a local extremum of f′(x). fx) Figure for 11
Problem refer to the graph of y = f(x) shown here. Find the absolute minimum and the absolute maximum over the indicated interval.[0, 8] f(x) 15 10 10
Find two numbers whose difference is 19 and whose product is a minimum.
Problem refer to the graph of y = f(x) shown here. Find the absolute minimum and the absolute maximum over the indicated interval.[2, 8] f(x) 15 10 10
Problem refer to the following graph of y = f(x):Identify the intervals on which f(x) is decreasing. fx) a d e
Find two numbers whose difference is 13 and whose product is a minimum.
Find two numbers whose sum is 19 and whose product is a maximum.
Problem refer to the following graph of y = f(x):Identify the intervals on which f(x) is increasing. fx) a d e
Problem refer to the following graph of y = f(x). Identify the points or intervals on the x axis that produce the indicated behavior.Local minima f(x) b C3 C6 C7 C4 C5 C2
In Problem round each expression to the nearest integer without using a calculator. 8
In Problem by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.m(x) = x3 on [-3, 1]
In Problem find the domain of the function and all x or y intercepts. x + 1 f(x) X - 2
In Problem inspect the graph of the function to determine whether it is concave up, concave down, or neither, on the given interval.The cube function, m(x) = x3, on (0, ∞)
Problem refer to the following graph of y = f(x). Identify the points or intervals on the x axis that produce the indicated behavior.Absolute maxima f(x) C1 C2 C3 CA C5 C6 C7 b -X
In Problem express the given quantity as a function f(x) of one variable x.The volume of a right circular cylinder of radius x and height equal to the radius
In Problem round each expression to the nearest integer without using a calculator. 1 2(1.01 - 1)
In Problem find the domain of the function and all x or y intercepts. x - 4 f(x) x + 3
In Problem by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.n(x) = √x on [3, 4]
In Problem inspect the graph of the function to determine whether it is concave up, concave down, or neither, on the given interval.The square root function, n(x) = √x, on (0, ∞)
In Problem express the given quantity as a function f(x) of one variable x.The volume of a right circular cylinder of diameter x and height equal to twice the diameter
In Problem by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.p(x) = 3√x on [-125, 216]
Problem refer to the following graph of y = f(x). Identify the points or intervals on the x axis that produce the indicated behavior.f(x) is increasing. f(x) b C3 C6 C7 C4 C5 C2
In Problem find the domain of the function and all x or y intercepts.f(x) = 3x + 36
In Problem express the given quantity as a function f(x) of one variable x.The product of two numbers x and y whose sum is 28
In Problem round each expression to the nearest integer without using a calculator. 5 0.01
Problem refer to the following graph of y = f(x). Identify the points or intervals on the x axis that produce the indicated behavior.f′(x) < 0 f(x) b C3 C6 C7 C4 C5 C2
In Problem by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.f(x) = x on [-2, 3]
In Problem find the domain of the function and all x or y intercepts. f(x) = V25 – x
In Problem round each expression to the nearest integer without using a calculator. 8 0.002
In Problem inspect the graph of the function to determine whether it is concave up, concave down, or neither, on the given interval.The square function, h(x) = x2, on (- ∞, ∞)
In Problem find the domain of the function and all x or y intercepts.f(x) = -4x - 28
Problem refer to the following graph of y = f(x). Identify the points or intervals on the x axis that produce the indicated behavior.The graph of f is concave downward. f(x) b C3 C6 C7 C4 C5 C2
In Problem express the given quantity as a function f(x) of one variable x.The sum of two numbers x and y whose product is 36
In Problem by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.g(x) = | x | on [-1, 4]
In Problem inspect the graph of the function to determine whether it is concave up, concave down, or neither, on the given interval.The identity function, f(x) = x, on (- ∞, ∞)
In Problem round each expression to the nearest integer without using a calculator. 3 1,000
In Problem find the domain of the function and all x or y intercepts. f(x) = V9 - x
In Problem express the given quantity as a function f(x) of one variable x.The area of a circle of diameter x
In Problem by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.h(x) = x2 on [-5, 3]
In Problem inspect the graph of the function to determine whether it is concave up, concave down, or neither, on the given interval.The cube function, m(x) = x3, on (- ∞, 0)
In Problem express the given quantity as a function f(x) of one variable x.The volume of a sphere of diameter x
In Problem round each expression to the nearest integer without using a calculator. 47 106
Problem refer to the following graph of y = f(x). Identify the points or intervals on the x axis that produce the indicated behavior.f′(x) appears to be 0. f(x) b C3 C6 C7 C4 C5 C2
Problem refer to the following graph of y = f(x). Identify the points or intervals on the x axis that produce the indicated behavior.f′(x) does not exist. f(x) b C3 C6 C7 C4 C5 C2
In Problem find the domain of the function and all x or y intercepts. 3 f(x) x? - 1 ||
In Problem round each expression to the nearest integer without using a calculator. In 100 100
In Problem find the domain of the function and all x or y intercepts. f(x) x² х2 + 5х + 4
In Problem inspect the graph of the function to determine whether it is concave up, concave down, or neither, on the given interval.The cube root function, p(x) = 3√x, on (- ∞, 0)
In Problem express the given quantity as a function f(x) of one variable x.The area of a rectangle of length x and width y that has a perimeter of 120 feet
Problem refer to the following graph of y = f(x). Identify the points or intervals on the x axis that produce the indicated behavior.Inflection points f(x) C1 C2 C3 CA C5 C6 C7 b -X
In Problem by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.q(x) = - 3√x on [27, 64]
In Problem round each expression to the nearest integer without using a calculator. es + 52
In Problem inspect the graph of the function to determine whether it is concave up, concave down, or neither, on the given interval.The absolute value function, g(x) = | x |, on (- ∞, 0)
In Problem by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.r(x) = -x2 on [-10, 11]
Use the graph of f in the figure to identify the following (assume that f″(0) < 0, f″(b) > 0, and f″(g) > 0):(A) The intervals on which f′(x) < 0(B) The intervals on which f′(x)
In Problem inspect the graph of the function to determine whether it is concave up, concave down, or neither, on the given interval.The cube root function, p(x) = 3√x, on (0, ∞)
Find two numbers whose sum is 13 and whose product is a maximum.
Problem refer to the graph of y = f(x) shown here. Find the absolute minimum and the absolute maximum over the indicated interval.[0, 10] f(x) 15 10 10
In Problem find h′(x), where f(x) is an unspecified differentiable function. In x h(x) f(x)
Find each limit in Problem. lim et - 1 - 4x
In Problem summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). 1 f(x) .2 1 +
In Problem explain why L’Hôpital’s rule does not apply. If the limit exists, find it by other means. x? lim x-3 (x + 3 5
In Problem find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.f(x) = -2x2 - 16x - 25
In Problem find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.f(x) = 5x2 - 10x - 3
In Problem find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x, y coordinates of the inflection points.f(x) = -x3 + 3x2
In Problem explain why L’Hôpital’s rule does not apply. If the limit exists, find it by other means. e* lim x0 In x X-
In Problem find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x, y coordinates of the inflection points.f(x) = x3 - 3x2 +
In Problem explain why L’Hôpital’s rule does not apply. If the limit exists, find it by other means. x? + 5x + 4 lim x + 1
In Problem summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x).f(x) = x - ln x
In Problem find (A) f′(x)(B) The partition numbers for f′(C) The critical numbers of f.f(x) = x2/3
In Problem summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). 2x f(x) 1 - x2
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