The greatest value of f(x) = (x + 1)1/3 - (x - 1)1/3 on [0, 1] is

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 Multiple Choice QuestionsMultiple Choice Questions

281.

Maximum value of f(x) = sin(x) + cos(x) is

  • 1

  • 2

  • 12

  • 2


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282.

The greatest value of f(x) = (x + 1)1/3 - (x - 1)1/3 on [0, 1] is

  • 1

  • 2

  • 3

  • 1/3


B.

2

Given, fx = x + 11/3 - x - 11/3      f'x = 13x + 1- 2/3 - 13x - 1- 2/3                = x - 12/3 - x + 12/33x2 - 12/3For maxima or minima, put f'(x) = 0 x - 12/3 = x + 12/3               x = 0     f'(x) does not exist atx = ± 1Clearly, f'(x)  0 for any other value of x  0, 1 Maximum value of f(x)= f(0) = 2.


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283.

The equation of normal to the circle 2x2 + 2y2 - 2 - 5y + 3 = 0 at (1, 1) is

  • 2x + y = 3

  • x - 2y = 3

  • x + 2y = 3

  • None of these


284.

The minimum value of the function f(x) = 2x3 - 21x2 + 36x - 20 is

  • - 128

  • - 126

  • - 120

  • None of these


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285.

If the function f(x) = 2x3 - 9ax2 + 12a + 1, where a > 0, attains its maximum and minimum values at p and q respectively such that p2 = q, then a equals

  • 3

  • 1

  • 2

  • 12


286.

For the function 3x4 - 8x3 + 12x2 - 48x + 25 in the interval [1, 3]. The value of maxima and minima are

  • 16, - 39

  • - 16, 39

  • 6, - 9

  • None of these


287.

f(x) = x3 - 27x + 5 is an increasing function when

  • x < - 3

  • x >3

  • x  - 3

  • x <3


288.

In the interval 0, π2 function log(sin(x)) is

  • increasing

  • decreasing

  • neither increasing nor decreasing

  • None of the above


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289.

A cone of maximum volume is being cut from sphere, then ratio between height of cone and diameter of sphere is

  • 23

  • 13

  • 34

  • 14


290.

The function x5 - 5x4 + 5x3 - 10 has a maximum, when x is equal to

  • 3

  • 2

  • 1

  • 0


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