# Calculus - Calculus MCQ

 A. x=1 B. x=-1 C. x=0 D. x= 1/√3 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
 A. 0 B. ∞ C. 1 D. -1 Option: A Explanation :
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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

 A. 1.9,2.2 B. 2.2,2.25 C. 2.25,2.5 D. None of these Option: B Explanation :
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The unit normal to the plane 2x +y + 2z = 6 can be expressed in the vector form as

 A. i3 + j2 + k2 B. C. D. Option: B Explanation :
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Maxima and Minima occur

 A. simultaneously B. once C. alternately D. rarely Option: C Explanation :