Find the function

Question

Find the function f given that the slope of the tangent line at any point (x, f(x))

 is f'(x)and that the graph of f passes through the given point.

f '(x) = 1 - (2x/(x^2+1) (0,9)

Answer 1

The indefinite integral ∫[1 - 2x/(x²+1)] dx = x - ln(x²+1) + C, so f(x) = x - ln(x²+1) + C. Since f(0) = 9, then 9 = C. Therefore, f(x) = x - ln(x²+1) + 9.