JEE Advanced 2010 Mathematics question
Let f be a function defined on (the set of all real numbers) such that , for all . If g is a function defined on with values in the interval such that , for all , then the number of points in at which g has a local maximum is
Answer: 1
Solution
, so , and since , has the same sign as ; g has a local maximum exactly where changes sign from positive to negative. The factors and are never negative, so they do not cause any sign change; the
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