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Question

The function f(x) = cot−1 x + x increases in the interval
(a) (1, ∞)
(b) (−1, ∞)
(c) (−∞, ∞)
(d) (0, ∞)

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Solution

(c) (−∞, ∞)

fx=cot-1x+xf'x=-11+x2+1 =-1+1+x21+x2 =x21+x20, xRSo, f(x) is increasing on -, .

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