Maximum and minimum
Introduction
Functions can achieve maximum and minimum values in an interval or in it's entire domain. An easy way to locate these maximums and minimums is by using the first and second derivative
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If a function has a maximum or a minimum, it can be found my inspecting the first derivative. A maximum or minimum can happen at any of these these places
- 1. Where the derivative equals to zero.
- 2. Where the derivative is undefined.
- 3. At an end point of the interval.
These are called critical points.
By using the second derivative test, we can classify each critical point to see if it is a max or a min.
The second derivative test:
if f ' ' (x) > 0 then it's concave up, and you have a minimum.
if f ' ' (x) < 0 then it's concave down, and you have a maximum.
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