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ans given in numerical for in my q ans is (-4, 3-root 21whole divided by 2 ) this bracket in close interval union open interval ( 1, infinity) as find p for which fn f(x) ( root under p+4/1-p - 1) x5-3x + ln5 decreases for all real x in this q, -1 is not part of root -1 is outside2- find interval in which at least 1 of the pts of local maxm of (cosx)2+ sinx lies
y=(cosx)2+sinxdy/dx=2cosx(-sinx)+cosx put dy/dx=0-2sinxcosx+cosx=0cosx[1-2sinnx]=0=> either cosx=0 or 1-2sinx=0=>x=pie/e or sinx=1/2=>x=pie/2 or pie/6d2y/dx2=-2cos2x-sinxd2y/dx2 at xpie/2=-2cospie-sinpie/2=2-1 =1>0so function is minima at x=pie/2d2y/dx2 at pie/6=-2cospie/3-sinpie/6 =-3/2 <0so function is maxima at pie/6Thanks & RegardsRinkoo GuptaAskIITians Faculty
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