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Maxima and Minima Made Easy!
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In mathematics, maxima and minima are points where a function reaches its highest or lowest value, either in a small neighborhood or over its entire domain.
1. Maximum (Maxima)
A maximum is a point where the function has the greatest value compared to nearby points.
Local or relative maximum: The function is larger at that point than at nearby values.
Global or absolute maximum: The function is larger at that point than at all other values in the domain.
2. Minimum (Minima)
A minimum is a point where the function has the least value compared to nearby points.
Local or relative minimum: The function is smaller at that point than at nearby values.
Global or absolute minimum: The function is smaller at that point than at all other values in the domain.
3. How to find maxima and minima:
For a differentiable function f(x):
Find the critical points where f′(x) = 0 or f′(x) is undefined.
Use the second derivative test:
If f′′(x) is greater than 0, the point is a local minimum.
If f′′(x) is less than 0, the point is a local maximum.
If f′′(x) = 0, the test is inconclusive.

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