Paragraph: Consider the function f : ( − ∞ , ∞ ) → ( − ∞ , ∞ ) defined by f ( x ) = x 2 + a x + 1 x 2 − a x + 1 ; 0

Question

Paragraph: Consider the function f : ( − ∞ , ∞ ) → ( − ∞ , ∞ ) defined by f ( x ) = x 2 + a x + 1 x 2 − a x + 1 ​ ; 0 < a < 2 Question: Which of the following is true?

TestHub · Accepted Answer

When x ∈ ( − 1 , 1 ) x 2 < 1 ⇒ x 2 − 1 < 0 ∴ f ′ ( x ) < 0 ⇒ f ( x ) is decreasing. Also, at x = 1 , f ′′ ( 1 ) = ( a + 2 ) 2 > 0 4 a ​ [ ∵ 0 < a < 2 ] ∴ f ( x ) has a local minimum at x = 1 .

Mathematics - Application of Derivative Question with Solution | TestHub

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