For $x \in \left( {0,{{5\pi } \over 2}} \right),$ define $f\left( x \right) = \int\limits_0^x {\sqrt t \sin t\,dt.} $ Then $f$ has

Question

local minimum at $\pi $ and $2\pi $

local minimum at $\pi $ and local maximum at $2\pi $

local maximum at $\pi $ and local minimum at $2\pi $

local maximum at $\pi $ and $2\pi $

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