Answer :
To find the relative extrema of a function, we need to find the points where the function reaches a local maximum or minimum value. To do this, we can start by finding the critical points of the function, which are the points where the derivative of the function is equal to zero or is undefined.
Once we have identified the critical points, we can use the second derivative test to determine whether each point is a relative maximum, a relative minimum, or neither. If the second derivative of the function is positive at a critical point, then the point is a relative minimum. If the second derivative is negative at a critical point, then the point is a relative maximum. If the second derivative is zero or does not exist at a critical point, then we cannot use the second derivative test and additional analysis is needed to determine the nature of the critical point.
It's important to note that the relative extrema of a function may not necessarily be the global extrema (i.e., the maximum and minimum values of the function over the entire domain). To find the global extrema, we need to consider the values of the function at the critical points as well as the values of the function at the endpoints of the domain (if applicable).
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