To determine the points of discontinuity of a function within a given interval, we need to check where the function violates one or more conditions from the continuity checklist.

Let's summarize the checklist:

1. $f(a)$ is defined — The function must have a value at the point $a$, meaning $a$ is in the domain of the function.
2. $\lim_{x \to a} f(x)$ exists — The limit of the function as $x$ approaches $a$ must exist.
3. $\lim_{x \to a} f(x) = f(a)$ — The value of the function at $a$ must equal the limit of the function as $x$ approaches $a$.

Steps to Identify Points of Discontinuity:

1. Find the Domain of the Function: Identify any points within the interval (1,6) where the function is not defined. These would be points where condition (1) is violated.
2. Check for Limits: For each point where the function is defined, evaluate whether the left-hand limit $\lim_{x \to a^-} f(x)$ and the right-hand limit $\lim_{x \to a^+} f(x)$ exist and are equal. If they are not, then condition (2) is violated.
3. Check for Function Value Matching the Limit: If the limit exists, check if $f(a) = \lim_{x \to a} f(x)$. If not, condition (3) is violated.

To proceed further and analyze the points of discontinuity, I need the specific function you're dealing with. Could you provide the function?

Would you like to continue with these steps?