Engineering Maths - Calculus

6. The minimum value of | x2  - 5x + 21 | is

  • Option : B
  • Explanation : Since value of a mod function cannot be less than zero, therefore f(x) = | x2 - 5x + 21 | is zero.
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7. The value of the improper integral

The value of the improper integral

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8. Value of the definite integral Value of the definite integral

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9. The function f(x) = 3x(x - 2) has a

  • Option : A
  • Explanation : f(x) = 3x (x - 2) = 3x- 6x Differentiating, we get   Again diferentiating,  For maxima or minima, - f '(x) =0 ∴  6x-6=0  ⇒ x=1 As f '(x) =6 >0 then f(x) is minimum at x=1
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10. What is the derivative of f(x) = | x | at x = 0

  • Option : D
  • Explanation : f(x) = |x| and f(x) = x for x > 0 ⇒f(x) = -x for x < 0 from the graph it is clear that derivative Hence from the graph it is clear that derivative doesn't exists for x=0
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