Let $f$ be the function whose graph goes through the point $(3, 6)$ and whose derivative is given by $f'(x) = \frac{1 + e^x}{x^2}$.
(a) Write an equation of the line tangent to the graph of $f$ at $x = 3$ and use it to approximate $f(3.1)$.
(b) Use Euler's method, starting at $x = 3$ with a step size of 0.05, to approximate $f(3.1)$. Use $f''$ to explain why this approximation is less than $f(3.1)$.
(c) Use $\int_{3}^{3.1} f'(x)\, dx$ to evaluate $f(3.1)$.