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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) asfind 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

keshav kr , 11 Years ago
Grade 12
anser 1 Answers
Rinkoo Gupta

Last Activity: 11 Years ago

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

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