To find absolute max or min
To find the absolute maximum or minimum of a function, we follow these steps:
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To find the absolute maximum or minimum of a function, we follow these steps:
1. Identify the domain: Determine the interval or set of values for which the function is defined.
2. Find critical points: Critical points are the locations where the derivative of the function is either zero or does not exist. To find critical points, we set the derivative of the function equal to zero and solve for the variable(s). Additionally, we need to check for any points where the derivative is undefined, such as vertical asymptotes.
3. Evaluate the function at critical points: Plug in the values of the critical points into the original function to find the corresponding function values.
4. Analyze the function behavior at the boundaries: If the function is defined on a closed interval, we need to consider the values of the function at the boundary points as well. Evaluate the function at each boundary point.
5. Determine the absolute maximum and minimum: Compare all the function values obtained from steps 3 and 4. The largest function value is the absolute maximum, and the smallest function value is the absolute minimum.
It’s important to note that the function must be continuous on the interval in consideration for these steps to be valid.
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