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Calculus

1. If

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2. The function f(x) = x3 - 6x2 + 9x + 25 has

  • Option : A
  • Explanation :

    f '(x) = 3(x2-4x+3)    f ''(x)=6(x)-12 at  x=1,  f "(1) at  x=3, f ''(3) = +ve

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3. The value of a = The value of a =

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4. The interval in which the Lagrange's theorem is applicable for the function f(x) = 1/x is

  • Option : C
  • Explanation : Since f(x) = (1/x) is not continuous in [- 3, 3] [- 4, 2] or [- 1, 1], The point of discontinuity is '0'. Only in [2, 3] the function is continuous, and differentiable hence mean value theorem is applicable in [2, 3].
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5. If f(x) = | x | , then for interval [-1, 1] ,f(x)

  • Option : C
  • Explanation : Since f(x) = |x| is continuous in [-1, 1] but it is not differentiable at x = 0 ε (-1, 1)
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