Question 10
Let $f: \mathbb{R} \to (0, \infty)$ be a continuous periodic function. Under the assumption that $2$ is a period of $f$, prove that:
a.
$$
\int_0^2 \frac{f(x+1)}{f(x)} \, dx \ge 2;
$$
b.
$$
\int_0^2 \frac{f(x+1)}{f(x)} \, dx = 2 \text{ if and only if } 1 \text{ is a period of } f.
$$
a.
$$
\int_0^2 \frac{f(x+1)}{f(x)} \, dx \ge 2;
$$
b.
$$
\int_0^2 \frac{f(x+1)}{f(x)} \, dx = 2 \text{ if and only if } 1 \text{ is a period of } f.
$$