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?

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    $\begingroup$ 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. $\endgroup$ – Koto Nov 28 '17 at 4:00
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    $\begingroup$ i can accept this answer if you'd like $\endgroup$ – mathguy Nov 28 '17 at 4:02
  • $\begingroup$ Let's wait for more creative people to show up. =D $\endgroup$ – 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.

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