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Let the range of the function f(x)= 1 2+ 3 x+ 3 x , x R be [a, b] . If and are respectively the A.M. and the G.M. of a and b , then is equal to

Options

  1. A2
  2. B2

Correct answer

3

Step-by-step solution

aligned & f(x) 1 2+ 3 x+ 3 x & [ 1 2+ 2 , 1 2- 2 ] & = a+b 2 a b = 1 2 ( a b + b a ) & = 1 2 ( 2- 2 2+ 2 + 2+ 2 2- 2 ) & = (2- 2 )+(2+ 2 ) 2 2 = 2 aligned

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