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AP EAMCET202125 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

If the function f(x)=a (x)+ 1 3 (3 x) attains maximum value at x= 3 , then a equals

Options

  1. A3
  2. B1 3
  3. C2
  4. D1 2

Correct answer

C. 2

Step-by-step solution

f(x)=a x+ 1 3 3 x aligned & f^ (x)=a x+ 1 3 3 x (3) d d x x= x & f^ (x)=a x+ 3 x & aligned At x= 3 , f(x) is maximum. f^ (x)=0 , at x= 3 Hence, a x+ 3 x=0 gathered a 3 + (3 3 )=0 a 1 2 +(-1)=0 a 2 =1 a=2 gathered

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