# How to find critical points when you get constant value

To find these critical points you must first take the derivative of the function. Second, set that derivative equal to 0 and solve for x. Each x value you find is known as a critical number.

But what happens if you take derivative and you get a constant value like -1?

• It means that your function is linear and its graph is a not horizontal infinite straight line, so it does not have any critical point. – Koto Nov 28 '17 at 4:00
• i can accept this answer if you'd like – mathguy Nov 28 '17 at 4:02
• Let's wait for more creative people to show up. =D – Koto Nov 28 '17 at 4:02

The definition of the derivative of a function is the rate of change of a function, say $f(x)$. It defines the gradient of the tangent at a specific point $x$. For a parabola, we visualise that the gradient is always changing, so the derivative of a parabola would be $f'(x) = ax+b$.
If the derivative of a function is a constant value, say, $2$, then this implies that the function's rate of change is $2$ through the whole function, for $x \in \mathbb R$. The only graph where this occurs is a linear graph, which is in the form $f(x) = ax+b$. This also happens to be the derivative of a parabola. Obviously, a line that extends infinitely in either direction does not have a critical point.