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COMEDK2025MathematicsApplication of DerivativesActual

If the function f(x)= x+ 1 3 3 x has its derivative equal to zero at x= 3 , then the value of ' ' is

Options

  1. A1
  2. B-1
  3. C2
  4. D0

Correct answer

C. 2

Step-by-step solution

The given function is f(x) = x + 1 3 3x . The derivative of the function is f'(x) = d dx ( x + 1 3 3x) = x + 1 3 3x 3 = x + 3x . It is given that f'(x) = 0 at x = 3 . Substituting x = 3 into the derivative expression: f'( 3 ) = ( 3 ) + (3 3 ) = 0 . Since ( 3 ) = 1 2 and ( ) = -1 , we have: ( 1 2 ) + (-1) = 0 . 2 = 1 . = 2 . Answer: 2

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