On the interval consider the function

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

On the interval (0,2π)(0,2\pi) consider the function h(x)=sin⁡x−xcos⁡xh(x)=\sin x-x\cos x. (i) Obtain all critical points of hh lying in (0,2π)(0,2\pi). (ii) Separate the interval (0,2π)(0,2\pi) into sub-intervals determined by these critical points and decide on each sub-interval whether hh is increasing or decreasing. (iii) Write down the exact coordinates of each local extremum of hh in (0,2π)(0,2\pi).

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