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daivinhtran
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Are inflection points critical points?
and what about at the value that f(x) undefined? Is that critical point too?
and what about at the value that f(x) undefined? Is that critical point too?
daivinhtran said:Are inflection points critical points?
and what about at the value that f(x) undefined? Is that critical point too?
A critical point is a point on a function where the derivative is equal to zero or undefined. It can also be defined as a point where the tangent line is horizontal or the slope of the function is changing.
To find critical points, you need to take the derivative of the function and set it equal to zero. Then, solve for the variable to find the x-values of the critical points. You can also use the second derivative test to confirm if the critical points are maximum, minimum, or inflection points.
Critical points are important in calculus because they represent the locations where the behavior of a function changes. These points can help us identify maximum and minimum values of a function and determine if the function is increasing or decreasing in a specific interval.
Yes, a function can have multiple critical points. This can happen when the function has multiple peaks and valleys, or when there are multiple points where the slope changes from positive to negative or vice versa.
No, not all critical points are local extrema. Some critical points can be inflection points, where the function changes from being concave up to concave down or vice versa. To determine if a critical point is a local extrema, we need to use the second derivative test or check the behavior of the function in the surrounding intervals.