Mathematics - Calculus

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11. Minimum point of the function

Minimum point of the function

is at

  • Option : A
  • Explanation : f'(x)= x2-1 For maximum and minimum value, f'(x) = 0 ∴ x2 -1= 0  x = ± 1 Again f(x) = 2x  At x = 1, f '(x) = 2 > 0  f '(x) = -2 < 0 Hence minimum at x = 1
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12. Minimum point of the function

is equal to

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13. If f (0) = 2 and f (x) = 1 /  (5-x2), then lower and upper bound of f(1) estimated by the mean value theorem are

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14. The unit normal to the plane 2x +y + 2z = 6 can be expressed in the vector form as

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15. Maxima and Minima occur

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