you don't know it?Math_QED said:Please define critical point.
mohammed El-Kady said:you don't know it?
thank youmathman said:" When dealing with functions of a real variable, a critical point is a point in the domain of the function where the function is either not differentiable or the derivative is equal to zero." definition from Wikipedia Looks like the answer is yes. (derivative discontinuous)
I don't know which definition the problem ask for. I know the definition of the derivative, but someone solved it with the differentiability , so i need to be sure from it.Math_QED said:Different people use different definitions... The answer to your question depends on the definition you are using.
The critical point of a piecewise function is a point where the function is not continuous, meaning there is a break or discontinuity in the graph. This can occur when the function changes from one defined equation to another, resulting in a sharp or abrupt change in the graph.
To find the critical point of a piecewise function, you need to first identify the points where the function changes from one equation to another. Then, you can evaluate the function at those points to determine if there is a discontinuity. If there is, that point is considered a critical point.
The critical point is important in a piecewise function because it can affect the behavior and interpretation of the function. It can also impact the domain and range of the function, as well as the continuity and differentiability of the function at that point.
Yes, a piecewise function can have multiple critical points. This can occur when there are multiple breaks or discontinuities in the graph, resulting in multiple points where the function is not continuous.
The critical point of a piecewise function can be used in real-world applications to analyze and model phenomena that involve sudden changes or discontinuities. This can include situations like phase changes in materials, abrupt changes in population growth, or changes in stock prices.