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Grade: 12
        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 outside
2- find interval in which at least 1 of the pts of local maxm of (cosx)2+ sinx lies
6 years ago

Answers : (1)

Rinkoo Gupta
askIITians Faculty
80 Points
							y=(cosx)2+sinx
dy/dx=2cosx(-sinx)+cosx
put dy/dx=0
-2sinxcosx+cosx=0
cosx[1-2sinnx]=0
=> either cosx=0 or 1-2sinx=0
=>x=pie/e or sinx=1/2
=>x=pie/2 or pie/6
d2y/dx2=-2cos2x-sinx
d2y/dx2 at xpie/2=-2cospie-sinpie/2=2-1
=1>0
so function is minima at x=pie/2
d2y/dx2 at pie/6=-2cospie/3-sinpie/6
=-3/2 <0
so function is maxima at pie/6
Thanks & Regards

Rinkoo Gupta

AskIITians Faculty
6 years ago
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