Determine the extrema of a function on a closed interval

👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points of a function under some certain condition is called the extreme value theorem. The extreme value theorem states that if a function is continuous on a closed interval [a, b], then f(x) has both a maximum and a minimum value on [a, b].

To obtain the extreme values of a function on a closed interval using the extreme value theorem, first, we obtain the critical values of the function on the interval by finding the derivative and solving for x. Next, we evaluate the function at each of the critical values found, then we also evaluate the function at each endpoint of the interval. The least of these values is the minimum value and the greatest is the maximum value.

Organized Videos:
✅Applications of the Derivative
✅Determine Increasing or Decreasing Function From a Table
✅Concavity of Functions
✅Extreme Value Theorem of Functions
✅First Derivative Test for Functions
✅Find the Critical Values of a Function
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
✅Sketch the Graph of the First and Second Derivative
✅Find the Points of Inflection of a Function
✅Second Derivative Test For a Function
✅Intermediate Value Theorem of Functions

Connect with me:

#derivatives #brianmclogan