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What is a Critical Point?

Critical Point

A critical point is a point on the graph of a function where the derivative is either zero or undefined. Critical points are important in calculus because they often correspond to local extrema (maxima or minima) or points of inflection of the function.

To find the critical points of a function, you typically start by finding its first derivative and then solving for the values of the independent variable where the derivative is zero or undefined. Once the critical points are identified, you can use various methods, such as the first derivative test, the second derivative test, or the concavity test, to determine the nature of the critical points (i.e., local maximum, local minimum, or point of inflection).

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