if f(x) is defined at c, and if either f'(c) is EQUAL to 0 or UNDEFINED then c is a ____
If f(x) is defined at c, and if either f'(c) is equal to 0 or undefined, then c is a critical point
If f(x) is defined at c, and if either f'(c) is equal to 0 or undefined, then c is a critical point.
A critical point is a point on the graph of a function where either the derivative of the function is equal to 0 or the derivative is undefined.
In calculus, the derivative of a function measures its rate of change at any given point. If the derivative is equal to 0 at a particular point, it means that the function has a horizontal tangent line at that point. This can represent either a local minimum or maximum, or an inflection point.
On the other hand, if the derivative is undefined at a point, it means that the function is not differentiable at that point. This typically occurs when there is a sharp corner or vertical tangent line at that point.
Therefore, when f'(c) is equal to 0 or undefined, c is considered a critical point of the function f(x).
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