Question

f(x)=3x-2/4x. Determinati primitiva F a functiei f caresatisface conditia F(1)=f(3)+f'(1)

Answer 1

Inteleg ca f( x ) = 3x - 2 / ( 4x ), adica 3x - 1 / ( 2x ) ;
Atunci F( x ) = 3x^2 / 2 - ( 1 / 2 )ln/x/ + k ;
Atunci F ( 1 ) = 3 / 2 + k ;
f( 3 ) = 9 - 1 / 6 = 53 / 6 ;
f'(x) = 3 - ( 1 / 2 )( - 1 / ( x^2) ) => f'(1) = 3 + 1 / 2 = 7 / 2 ;
Avem relatia 3 / 2 + k = 53 / 6 + 7 / 2 <=> k = 53 / 6 + 2 = 65 / 6 ;
In final, F( x ) = 3x^2 / 2 - ( 1 / 2 )ln/x/ + 65 / 6 ;

Bafta !