Let y = f(x) be a particular solution of the differential equation dy/dx = 1 / xy with f(1) = 2. (a) Find d2y dx2 at the point (1, 2).
(b) Write an equation for the line tangent to the graph of f at (1, 2) and use it to approximate f(1.1). Is the approximation for f(1.1) greater than or less than f(1.1)? Explain your reasoning.
(c) Find the solution of the given differential equation that satisfies the initial condition f(1) = 2.