Learn how to find maximum & minimum values of a function on a closed interval

Finding the maximum or minimum values of a function on a closed interval (sometimes referred to as finding ‘local extrema’) is a common application of derivatives. It’s essentially finding the highest and lowest points on the graph of the function, looking at a particular section of the graph. Although students often find this technique intimidating, it’s actually quite straight-forward with some practice. The technique centers around being about to find Stationary Points. Any questions about this video drop us a message HERE.

  Key Points

Closed intervals are ranges of values which include the endpoints of the range

Open intervals, on the other hand, do not include the endpoints

Maximum and minimum values are the greatest and least ‘Y’ value in the closed interval

The max and min values correspond to the highest and lowest point on the graph

The max and min values always occur at a stationary point or at an endpoint

Find the stationary points and test their ‘Y’ values. Test the ‘Y’ values of the endpoints.

Then compare all of the values to find the greatest and the least, which are the max and min values

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