I NEED ANSWER URGENTLY....so I can have peace of mind

What is f(x) if f ''(x) = 9/x^2, f(1)=5 and f'(1) = 7
Thank YOU :)

f''(x) = 9x^(-2)
f'(x) = -9x^(-1) + C
f'(1) = -9(1^(-1)) + C = 7
f'(1) = -9 + C = 7
C = 16
f'(x) = -9x^(-1) + 16
f(x) = -9 ln x + 16x + C
f(1) = -9 ln (1) + 16(1) + C = 5
-9 ln 1 + 16 + C = 5
-9(0) + 16 + C = 5
C = -11
f(x) = -9 ln x + 16x - 11

Answer: f(x) = -9 ln x + 16x - 11

http://www.wolframalpha.com/
f(1)=5