Which one of the following is correct in respect of the function

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 Multiple Choice QuestionsMultiple Choice Questions

11.

Let fx = x + 1x, where x  (0, 1). Then which one of the following is correct ?

  • f(x) fluctuates in the interval

  • f(x) increases in the interval

  • f(x) decreases in the interval

  • None of the above


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12.

Which one of the following is correct in respect of the function f(x) = x(x - 1)(x + 1) ?

  • The local maximum value is larger than local minimum value

  • The local maximum value is smaller than localminimum value

  • The function has no local maximum

  • The function has no local minimum


A.

The local maximum value is larger than local minimum value

      fx = xx2 - 1     f'x = 22x  x2 - 1 = 3x2 - 1    f''x = 6xAt f'0 = 0  x = ± 13fxmax = f - 13 =  - 1313 - 1 = 233fxmin = f13 = 1313 - 1 =  - 233


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13.

Consider the function

fx = x - 1 + x2

where, x  

Which one of the following statements is correct ?

  • f(X) has local minima at more than one point in  - , 

  • f(x) has local maxima at more than one point in  - , 

  • f(x) has local minimum at one point only in  - , 

  • (x) has neither maxima nor minima in  - , 


14.

Consider the function

fx = x - 12x + 1x  - 23

What is the number of points of local minima of the function f(x) ?

  • None

  • One

  • Two

  • Three


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15.

Consider the function

fx = x - 12x + 1x  - 23

What is the number of points of local maxima of the function f(x) ?

  • None

  • one

  • Two

  • Three


16.

Consider the function

f(x) = x3sinxcosx6 - 10pp2p3

where, p is a constant

What is the value of f'(0) ?

  • P3

  • 3P3

  • 6P3

  •  - 6P3


17.

Consider the function

f(x) = x3sinxcosx6 - 10pp2p3

where, p is a constant

What is the value of P for which f''(0) = 0 ?

  •  - 16 or 0

  •  - 1 or 0

  • - 16 or 1

  •  - 1 or 1


18.

Which one of the following statements is correct irespect of the function

f(x) = x3sin(x) ?

  • It has local maximum at x = 0

  • It has local minimum at x = 0

  • It has neither maximum nor minimum at x = 0

  • It has maximum value 1


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19.

fx = 3x2 + 12x - 1, - 1  x  237 - x,                  2 < x  3 

Which of the following statements is/are correc

  1. f(x) is increasing in the interval [1, 2].
  2. f(x) is decreasing in the interval [2, 3]

Select the correct answer using the code given below :

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


20.

What is the value of k for which the sum of the squares of the roots of 2x2 – 2(k 2)x – (k + 1) = 0 is minimum ?

  • - 1

  • 1

  • 32

  • 2


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