MHT CET2018MathematicsApplication of Derivatives

If f x = x x 2 + 1 is increasing function then the value of x lies in

Options

AR
B- ∞ , - 1
C1 , ∞
D- 1 , 1

Correct answer

D. - 1 , 1

Step-by-step solution

f ( x ) = x x 2 + 1 f ' ( x ) = ( x 2 + 1 ) − x ( 2 x ) ( x 2 + 1 ) 2 = − x 2 + 1 ( x 2 + 1 ) 2 Since f(x) is increasing function, f ' ( x ) > 0 ∴ ( − x 2 + 1 ) > 0 as x 2 + 1 is always positive ∴ x 2 − 1 < 0 ∴ ( x − 1 ) ( x + 1 ) < 0 ∴ x ∈ ( − 1 , 1 )

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