Q.

Let f(x)=(x4)(x5)(x6)(x7) then

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a

the equation f’(x)=0 has only one root  

b

f’(x)=0 has four roots

c

three roots of  f’(x)=0 lie in 4,55,66,7

d

three roots of  f’(x)=0 lie in 3,44,55,6

answer is B.

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Detailed Solution

f(4)=f(5)=f(6)=f(7)=0By Rolle's theroem
α1(4,5),α2(5,6),α3(6,7)such that 
f'(αi)=0, i=1,2,3
 

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