Functional Relation

Calculus Level 3

Let f ( x + y 2 ) = f ( x ) + f ( y ) 2 f(\frac{x+y}{2} )=\frac{f(x) +f(y)}{2} for all real x , y x,y . If f ′ ( 0 ) = − 1 , f ( 0 ) = 1 f'(0) = -1, f(0) = 1 , find f ( 2 ) f(2) .

-1 2 1 0

Shivam Jadhav by Shivam Jadhav , 22, India

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1 solution

Shivam Jadhav
Apr 5, 2015

Diffrentiate the function. We get f ( x ) = 1 − x f(x) = 1 - x . Therefore f(2) = -1.

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