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Question

If Rolle's theorem holds true for the function f(x)=2x3+bx2+cx, x[1,1] at the point x=12, then (2b+c) is equal to 


A
1
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B
1 
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C
2 
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D
3
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Solution

The correct option is B 1 
Since, Rolle's theorem holds true for f(x) in the interval [1,1]
f(1)=f(1)
2+b+c=2+bc2c=4
or, c=2
f(12)=0
f(x)=6x2+2bx+c
f(12)=64+b+c=0b+c=32
or, b=12

2b+c=12=1

Mathematics

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