Q:

Calculus/ zero or undefined ? with explanation

How can I know if the it suppose to be zero or undefined, because when I try to substitute in the original equation with 5/2 I will end up with a number and y. Same goes to (c) I will end up with x. So what shall I do? 
It is more important to know the explanation rather than just the answer :) thanks in advance

A:

A tangent that is horizontal line at a given point, (in the first case), has slope zero, and so $dy/dx = 0$ at $x = 5/2$.
In the latter case, you will have that $dy/dx$ is undefined. Just substitute $y = -13/2$ into the equation for $dy/dx$ to see that the denominator of $dy/dx$ is then equal to $0$ at that value, and so $dy/dx$ is undefined there, since we cannot have division by zero.

