JEE Advanced Mathematics question
Let be a function defined on , the set of real numbers, such that
f'(x) = 2010(x - 2009)(x - - - for all x .
If is a function defined on with values in such that for all then the number of points in at which has a local maximum is
Answer: 1
Solution
, so has the same sign as (equivalently, and have the same local extrema since is increasing). The critical points are . Sign changes of come only from the odd-power factors and :
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