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mathematics
college mathematics for business economics

Questions and Answers of College Mathematics For Business Economics

In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = x² + x = 2 x²
In Problems 33-46, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.f(x) = 2x3 - 3x2 - 36x
Find each limit in Problems 31–40. In (1 + 6x) lim xln(1 + 3x)
In Problems 31–40, 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 coordinates of the inflection points. f(x) =
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. In(x -
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function. f(x) = 2x x² + 1 2
In Problems 33-46, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x) = -2x³ + 3x² + 120x
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). zł 9-xç - zx f(x)
Find each limit in Problems 31–40. In(1 + 6x) lim x-0ln(1 + 3x)
In Problems 31–40, 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 coordinates of the inflection points. f(x) =
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule.
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function. f(x) = -8.x 1²+ 4 X
In Problems 33-46, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x) = 3x4 - 4x³ + 5
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). x² x - 1
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule.
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function. f(x) = x² - 1 x² + 1
In Problems 33-46, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x) = x4 + 2x²³ +5
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) || 1² 2 + x
In Problems 41-48, f(x) is continuous on (-∞,∞). Use the given information to sketch the graph of f. f'(x) X f(x) f(x) ++- -4 0 0 + + + -2 -2 -2 + +++0 - -1 -1 + + + + 0 + + + 1 2 --- 0 0 - 0
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. lim x-0 In(1 +
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function. f(x) 9-1² x² + 4
In Problems 33-46, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x) = = (x (x - 1)ex
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 3x²+2 1² - 9
In Problems 41-48, f(x) is continuous on (-∞,∞). Use the given information to sketch the graph of f. X f(x) -3 -4 f'(x) +++ ND + + + 0. f"(x) +++ ND- 0 0 0 - -- - 1 2 2 1 IN - 0 ++++ 4 -1 0 + +
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) 2x² + 5 4 - x²
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. lim x-0 In(1
In Problems 33-46, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x) = x ln x - x
Use the second-derivative test to find any local extrema for f(x) = 3 - 3x² 16x + 200
In Problems 41-48, f(x) is continuous on (-∞,∞). Use the given information to sketch the graph of f. -4 f(x) 0 X f'(x) +++ 0 f"(x) -2 -2 3 0 0 -- ND 2 -2 -- 4 0 + + + + + + + + 0 = - ND + + + + +
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. lim x-0 In(1 +
In Problems 33-46, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x) = 4x¹/3-2/3
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = x³ x 2
In Problems 41-48, f(x) is continuous on (-∞,∞). Use the given information to sketch the graph of f. f(0) = 2,f(1) = 0, f(2) = -2; f'(0) = 0,f'(2) = 0; f'(x) > 0 on (-∞, 0) and (2, ∞); f'(x)
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. x² + 2x +
In Problems 33-46, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x) =(x² - 9) 2/3
In Problems 43-66, find the indicated extremum of each function on the given interval. Absolute minimum value on [0, ∞ ) for f(x) = x² - 6x²
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) 13 4- x
In Problems 41-48, f(x) is continuous on (-∞,∞). Use the given information to sketch the graph of f. f(-2) = -2,f(0) = 1,f(2)= 4; f'(-2) = 0, f'(2) = 0; f'(x) > 0 on (-2, 2); f'(x) 0 on (-∞0,
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. 2x³ lim x1
In Problems 43-66, find the indicated extremum of each function on the given interval. Absolute minimum value on [0, ∞ ) for f(x) = (x + 4)(x - 2)²
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = (3x) et
In Problems 41- 48, f(x) is continuous on (-∞,∞). Use the given information to sketch the graph of f. f(-1) = 0,f(0) = -2, f(1) = 0; f'(0) = 0, f'(-1) and f'(1) are not defined; f'(x) > 0 on (0,
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. x³ +
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. lim x 3 x³ +
In Problems 43-66, find the indicated extremum of each function on the given interval. Absolute minimum value on [0, ∞) for f(x) = (2x) (x + 1)²
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x).f(x) = (x - 2) ex
In Problems 47-52, use a graphing calculator to approximate the critical numbers of f(x) to two decimal places. Find the intervals on which f(x) is increasing, the intervals on which f(x) is
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. x³ - 12x +
In Problems 43-66, find the indicated extremum of each function on the given interval. Absolute maximum value on (0, ∞ ) for f(x) = 2x4 -8r³
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). -0.57 f(x) = e
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). (x-2)(x² - 4x - 8) f(x) = (x - 2) (x²
In Problems 47-52, use a graphing calculator to approximate the critical numbers of f(x) to two decimal places. Find the intervals on which f(x) is increasing, the intervals on which f(x) is
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. x³ + x² = x
In Problems 43-66, find the indicated extremum of each function on the given interval. Absolute maximum value on (0, ∞ ) for f(x) = 4x³ -
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). -21² f(x) = e =²₁²
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = (x − 3)(x² - 6x - 3)
In Problems 47-52, use a graphing calculator to approximate the critical numbers of f(x) to two decimal places. Find the intervals on which f(x) is increasing, the intervals on which f(x) is
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. lim 3x² +
Discuss the difference between a partition number for f'(x) and a critical number of f(x), and illustrate with examples.
In Problems 43-66, find the indicated extremum of each function on the given interval. Absolute maximum value on (0, ∞) for 12 f(x) 20 - 3x X
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = (x + 1) (x² - x + 2)
Find the absolute maximum for f'(x) ifGraph f and f' on the same coordinate system for 0 ≤ x ≤ 4. f(x) = 6x² x³ + 8
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. lim X-0 4x² +
In Problems 43-66, find the indicated extremum of each function on the given interval. Absolute minimum value on (0, ∞ ) for 9 f(x) = 4 + x + X
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) In x X
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x)= (1-x) (x² + x + 4)
Find two positive numbers whose product is 400 and whose sum is a minimum. What is the minimum sum?
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule.
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = -0.25x4 + x³
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. 3.x lim x-00
In Problems 43-66, find the indicated extremum of each function on the given interval. Absolute maximum value on (0, ∞ ) for 250 x² f(x) = 20 - 4x -
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = x ln x
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 0.25x4 - 2x³
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 1 x² + 2x 8
In Problems 53-60, find the intervals on which f(x) is increasing and the intervals on which f(x) is decreasing. Then sketch the graph. Add horizontal tangent lines.f(x) = 2x2 - 8x + 9
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. 1 +
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 16x(x - 1)³
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = x³ ²-12
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule.
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = -4x(x + 2)³
In Problems 53-60, find the intervals on which f(x) is increasing and the intervals on which f(x) is decreasing. Then sketch the graph. Add horizontal tangent lines.f(x) = x3 - 12x + 2
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) || 3-x²
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. lim x→%
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = (x² + 3) (9-x²)
In Problems 43 - 66, find the indicated extremum of each function on the given interval. Absolute maximum value on (0, ∞ ) for f(x) = ln(x²ex)
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. lim x→ In (1
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = (x² + 3)(x² - 1)
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) || x³ 1² - 12
A company manufactures and sells x cell phones per month. The monthly cost and price–demand equations are, respectively, (A) Find the maximum revenue. (B) How many phones should the company
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule.
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = (x²-4)²
In Problems 43 - 66, find the indicated extremum of each function on the given interval. Absolute minimum value on (0, ∞ ) for f(x) X
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule.
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = (x² - 1) (x² - 5)
In Problems 59-66, show that the line y = x is an oblique asymptote for the graph of y = f(x), summarize all pertinent information obtained by applying the graphing strategy, and sketch the graph of
A 100-apartment building in a city is fully occupied every month when the rent per month is $500 per apartment. For each $40 increase in the monthly rent, 5 fewer apartments are rented. If each
In Problems 43 - 66, find the indicated extremum of each function on the given interval. Absolute maximum value on (0, ∞ ) for f(x) = 5x 2x ln x
In Problems 61-68, f(x) is continuous on (-∞, ∞ ). Use the given information to sketch the graph of f. f'(x) +++ 0 + + + 0- - - x T— -2 -1 -1 1 0 2 1 3 2 20 1
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 3x55x4
In Problems 59–66, show that the line y = x is an oblique asymptote for the graph of y = f(x), summarize all pertinent information obtained by applying the graphing strategy, and sketch the graph

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