Are endpoints also critical points?
I'm trying to find the critical points of a function on the interval [-1,5]. So far,the only critical point I have is 2. Does that mean -1 and 5 are also critical points?
only if it is horizontal there.
http://www.google.com/search?q=critical+point+of+function&ie=utf-8&oe=utf-8
I hope it was not you who posted this earlier, where I explained it all.
http://www.jiskha.com/display.cgi?id=1489049850
Yeah, how dare I ask for clarification on something I'm trying to understand.
Endpoints, such as -1 and 5 in the case of the interval [-1,5], are not considered critical points in the context of finding the critical points of a function.
Critical points are the values within the interval where the derivative of the function is either zero or undefined. They represent the potential locations of local extrema (minima or maxima) and inflection points on the function.
To find critical points in a given interval, follow these steps:
1. Differentiate the function with respect to the variable in question.
2. Set the derivative equal to zero and solve for the variable. Note any values that make the derivative undefined as well.
3. Check the values obtained from step 2, along with the endpoints of the interval, to determine if they are critical points by evaluating whether they meet the criteria for minima, maxima, or inflection points.
In your case, if you have found 2 as the only value that makes the derivative zero within the interval [-1,5], then 2 is the only critical point within that interval. The endpoints -1 and 5 are not considered critical points because they are not potential locations of local extrema or inflection points.