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Solved Examples
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ff  Find the absolute extrema value of f(x) = xx2+1 on [0, 3].
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ff  The total surface area of an open rectangular box with square base is 36 ft2. Find the largest possible volume of the box.
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ff  Find the absolute maximum and absolute minimum values for the function f(x) = ex(1 + x2) on [- 2, 2].  ff View Solution
ff  Find the two non - negative numbers that add upto 66 and such that their product is as large as possible.
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ff  Find the absolute extreme of f(x) = 1-xx2+3 on [- 2, 5].  ff View Solution
ff  Find the two numbers whose sum is k and the sum of their squares is minimum.  ff View Solution
ff  Maria has a rectangular backyard. She wants to grow four types of flowers in her yard. She divided the yard into four equal, and parallel portions using a 1000 ft fencing. What dimensions should be used so that the enclosed area will be a maximum?
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ff  Which of the following statements are correct for the function f(x) = x2 + 2x + 5 on the interval [- 1, 3]?
I. f(x) has maximum value at x = 3
II. f(x) has minimum value at x = - 1
III. f(x) has maximum value at x = 0
IV. f(x) has minimum value at x = 2  ff
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ff  Find the absolute minimum value of f(x) = x(5x-6)2 on [- 2, 0].  ff View Solution
ff  Find the two positive numbers whose product is 36 and sum is a minimum.  ff View Solution
ff  Find two numbers such that their product is maximum, if the sum of one number and twice the other is 4.
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ff  A farmer has 2000 meters of fencing and wanted to fence a rectangular field used for livestock that borders his house on one side. He needs no fencing along his house. What will be the dimensions of the field if the area is to be largest?
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ff  Which of the following are the absolute extrema for f(x) = sin x + cos x on [0, π3]?  ff View Solution
ff  Find the two numbers x and y which satisfy the condition - 12x+π4y = 1 and for which p = xy is a minimum.  ff View Solution
ff  Find the absolute extrema of f(x) = x4 - 32x3 on [- 1, 2].  ff View Solution
ff  Fifty members of a music club, planned to go on a tour to a nearby hill station. The tour costs $1000 per person. A discount of $10 can be availed by each touring member for every additional member. How many people to be added to the existing group in number (not more than 50) in order to avail the maximum discount?
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ff  Find a point on x - axis which minimises the sum of the squares of the distances from it to the points (0, 0) and (3, 2).  ff View Solution
ff  Which of the following statements are correct for the function f(x) = x3 - 3x2 + 2x + 1 on the interval [- 4, 0]?
I. f(x) has maximum value at x = 0
II. f(x) has minimum value at x = - 4
III. f(x) has minimum value at x = - 1
IV. f(x) has maximum value at x = - 2
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ff  Which of the following statements are correct for the function f(x) = e2x + 5 on the interval [- 4, 3]?
I. f(x) has maximum value at x = 3
II. f(x) has minimum value at x = - 4
III. f(x) has maximum value at x = - 3
IV. f(x) has minimum value at x = 0
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ff  Which of the following statements are correct for the function f(x) = (x - 3) (x + 2) on the interval [- 5, 2]?

I. f(x) has maximum value at x = - 5
II. f(x) has minimum value at x = 2
III. f(x) has minimum value at x = 0.5
IV. f(x) has maximum value at x = - 3
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ff  Which of the following statements are correct for the function f(x) = ln (x2 + 3) on the interval [- 10, 10]?
I. f(x) has minimum value at x = 0
II. f(x) has maximum value at x = 10
III. f(x) has maximum value at x = - 10
IV. f(x) has minimum value at x = - 10
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ff  Which of the following statements is true for the function f(x) = 2x + 3 on the interval [- 5, 4]?
I. f(x) has maximum value at x = 4
II. f(x) has minimum value at x = - 5
III. f(x) has minimum value at x = 0
IV. f(x) has maximum value at x = - 5  ff
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ff  Which of the following statements are correct for the function f(x) = x+1x2+2 on the interval [- 3, 5].
I. f(x) has maximum value at x = 0.8
II. f(x) has minimum value at x = - 3
III. f(x) has maximum value at x = 0
IV. f(x) has minimum value at x = 2  ff
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BBB Which of the following statements are correct for the function f(x) = 2x + ex2 on the interval [- 8, 4].
I. f(x) has maximum value at x = 4
II. f(x) has minimum value at x = - 8
III. f(x) has maximum value at x = 0
IV. f(x) has minimum value at x = 4
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BBB Which of the following statements are correct for the function f(x) = sin x + cos x on the interval [- π, π]?
I. f(x) has maximum value at x = π4
II. f(x) has minimum value at x = -3π4
III. f(x) has maximum value at x = 0
IV. f(x) has minimum value at x = - π
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BBB Which of the following statements are correct for the function f(x) = x3-1x(x+2) on the interval [- 10, - 3]?
I. f(x) has maximum value at x = - 10
II. f(x) has minimum value at x = - 1.2
III. f(x) has maximum value at x = - 4.1
IV. f(x) has minimum value at x = - 10
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BBB Find the absolute maximum value of f(x) = ln (x2 + 2x + 4) on [- 4, 3].
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BBB Find the absolute minimum value of f(x) = (x+1)23 on [- 3, 4]. BBB View Solution
BBB Which of the following is the absolute maximum value of f(x) = x2 (ln x) on [1, 3]? BBB View Solution
BBB Find the absolute maximum value of f(r) = 1-rr2+1 on [- 2, 3]. BBB View Solution
BBB Find the absolute maximum value of f(x) = 20 - 24x - 15x2 - 2x3 on [- 5, 3]. BBB View Solution
BBB Which of the following is the absolute minimum of f(x) = 2 ln (x2 + 3) - x on [- 3, 5]? BBB View Solution
BBB Find the absolute extrema of f(x) = esin x - e- sin x on [0, 3π4].
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BBB Which of the following is the absolute maximum of f(x) = x2-2x+9x2+2x+9 on [- 4, 7]?
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BBB Which of the following is the absolute maximum of f(x) = x2(3 - x) on [- 2, 4]? BBB View Solution