Extreme Value Theorem
To find inflection points1. Find the second derivative2. Set the second derivative equal to zero3. Solve for xOptional4. Plug in and solve for f(x)
The Extreme Value Theorem states that for a continuous function defined on a closed interval, there exists at least one point on the interval, such that the function takes its maximum and minimum values.
In other words, if f(x) is continuous on the closed interval [a,b], then there exists at least one c in [a,b] such that f(c) is the absolute maximum value and at least one d in [a,b] such that f(d) is the absolute minimum value.
This theorem is very useful in applications such as optimization problems because it guarantees the existence of a maximum or minimum value.
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