Statement-1: The function x 2 ( e x + e − x ) is increasing for all x 0 . Statement-2: The functions x 2 e x and x 2 e − x are increasing for all x 0 and the sum of two increasing functions in any

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Statement-1: The function x 2 ( e x + e − x ) is increasing for all x > 0 . Statement-2: The functions x 2 e x and x 2 e − x are increasing for all x > 0 and the sum of two increasing functions in any interval ( a , b ) is an increasing function in ( a , b ) .

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Let y = x 2 ⋅ e − x For increasing function, d x d y > 0 ⇒ x [ ( 2 − x ) e − x ] > 0 ∵ x > 0 , ∴ ( 2 − x ) e − x > 0 ⇒ ( 2 − x ) e x 1 > 0 For 0 < x < 2 , ( 2 − x ) < 0 ∴ e x 1 < 0 , but it is not possible Hence the statement- 2 is false.

Mathematics - Application of Derivative Question with Solution | TestHub

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