Find all real numbers A ,B such that the function f(x) = A.2x + B, satisfies the conditions f'(1) = 2 and R 3\n0 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
B = -2/3

Thanks
Bharat Bajaj
askiitians faculty
IIT Delhi

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 B = -2/3