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Q.

For  f(x)=lnx2+α7x  Roll's theorem is applicable on  [3, 4] with  c(3,4)  such that  f(c)=0 The value of  f′′(c) is

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a

16

b

112

c

16

d

112

answer is A.

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Detailed Solution

Roll's theorem is applicable to  f(x)=lnx2+α7x on [3,4]

     f(3)=f(4)     ln9+α21=ln16+α28

 9+α21=16+α2836+4α=48+3αα=12

Now,  f(x)=lnx2+α7x

 f(x)=lnx2+12ln7x f(x)=2xx2+121x=x212xx2+12 f(x)=0x212=0x=±12 c=12

Now,  f(x)=x212xx2+12

xx2+12f′′(x)=2x2x2+12x212x2+12+2x2x2x2+122f′′(x)=x4+48x2+144x2x2+122f′′(12)=112

 

 

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