gassi said:
A critical point is a point on a graph where the derivative is equal to zero or does not exist. It is also known as a stationary point.
To find critical points on a graph, you must first find the derivative of the function. Then, set the derivative equal to zero and solve for the variable. The resulting values are the critical points.
Critical points are important because they represent the maximum, minimum, or inflection points on a graph. They help us understand the behavior of a function and can be used to find the optimal values for a given problem.
A relative critical point is a point where the derivative is equal to zero, while an absolute critical point is a point where the derivative does not exist. Relative critical points can be local maxima or minima, while absolute critical points are global maxima or minima.
To determine the nature of a critical point, you can use the second derivative test. If the second derivative is positive at the critical point, it is a local minimum. If the second derivative is negative, it is a local maximum. If the second derivative is zero, the test is inconclusive and you may need to use other methods to determine the nature of the critical point.