Find all real numbers A , B such that the function f (x) = A.2x + B, satisfies the conditions f ' (1) = 2 and 3 0 f (x)dx = 7.

Differentiate the function :
f`(x) = 2A
f`(1) = 2A = 2
Hence, A = 1
Integrate the function :
Ax^2 + Bx : 0 to 3 = 7
9A + 3B = 7
9 + 3B = 7