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KCET2017MathematicsLimits

The value of ( C ) in Mean value theorem for the function ( f(x)=x² ) in ( [2,4] ) is

Options

  1. A( 03 )
  2. B( 02 )
  3. C( 04 )
  4. D( 77 / 2 )

Correct answer

B. ( 02 )

Step-by-step solution

We know that, value of ( C ) in mean value theorem for the function ( f(x) ) in ( [a, b] ) is given by ( C= f^ (b)-f^ (a) b-a ) Here ( f(x)=x² ) and ( [a, b] ) is ( [2,4] ). Then, ( C= 2(4)-2(2) 4-2 ) ( = 8-4 2 =2 )

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