Critical point
Where f'(p) doesn’t exist or where f'(p)=0
A critical point is a point on a graph where the derivative of a function is equal to zero or does not exist. In other words, it is a point where the slope of the graph changes from positive to negative, or vice versa. Critical points can occur at local maximums, local minimums, or at points of inflection.
To find critical points, we need to take the derivative of the function and solve for when it equals zero or when it does not exist. Once we have found the critical points, we can analyze the behavior of the function on either side, to determine if it is increasing or decreasing.
The behavior of a function at its critical point can tell us a lot about the nature of the function. If it is a local maximum, the function will increase before the critical point and decrease after the critical point. If it is a local minimum, the function will decrease before the critical point and increase after the critical point. If it is a point of inflection, the function will be changing concavity (from concave up to concave down, or vice versa).
Critical points are important in calculus, as they are used to find the maximum and minimum values of a function and to determine points of inflection. They also play an important role in optimization problems.
More Answers:
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