Let f(x) = x + x^-1 . Then which of the following is correct? - Mathematics MCQ Mathematics Mock Test - 2 2026 | ExamTest.live

mediumMCQMathematics Mock Test - 22026Mathematics

1 attempts0% success rate1 mark

Let f (x) = x + x^{- 1} . Then which of the following is correct?

Solution & Step-by-step Explanation

Given f (x) = x + \frac{1}{x} .Find the derivative: f^{'} (x) = 1 - \frac{1}{x ^{2}} .Set f^{'} (x) = 0 for critical points: 1 - \frac{1}{x ^{2}} = 0 ⟹ x^{2} = 1 ⟹ x = \pm 1 .Find second derivative: f^{''} (x) = \frac{2}{x ^{3}} .At x = 1 : f^{''} (1) = 2 > 0 (Local Minimum).Minimum value f (1) = 1 + \frac{1}{1} = 2 .At x = - 1 : f^{''} (- 1) = - 2 < 0 (Local Maximum).Maximum value f (- 1) = - 1 + \frac{1}{- 1} = - 2 .Here, Local Maximum (- 2) < Local Minimum (2) .Thus, max f (x) < min f (x) .

Try it yourself before checking the explanation above.

Let f (x) = x + x^{- 1} . Then which of the following is correct?

f (x) has a maximum but no minimum

f (x) has a maximum and a minimum and max f (x) > min f (x)

f (x) has a maximum and a minimum and max f (x) < min f (x)

f (x) has a minima but no maxima

Practice with timed mock tests and track your performance across Mathematics.