QJEEAdv08Ma2248: JEE Advanced 2008 Mathematics - Class 12 JEEAdv08Ma2248 Solution: Which of the following is true?

Question

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Which of the following is true?

A f(x) is decreasing on (−1,1) and has a local minimum at x=1
B f(x) is increasing on (−1,1) and has a local minimum at x=1
C f(x) is increasing on (−1,1) but has neither a local maximum nor a local minimum at x=1
D f(x) is decreasing on (−1,1) but has neither a local maximum nor a local minimum at x=1

Accepted Answer

As when $x \in (- 1, 1), f^{'} (x) < 0$

So, f(x) is decreasing on ( $- 1, 1$ ) at x = 1

$f^{″} (1) = \frac{4 a}{{(a + 2)}^{2}} > 0$

So, local minima at x = 1

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