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education/math/MATH1210 (calc 1)/Max and Min.md
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# Absolute Maximum/Minimum # Maximum/Minimum
A function $f$ has an *absolute maximum* at $c$ if $f(c) >= f(x)$. We call $f(c)$ the maximum value of $f$. A function $f$ has an *absolute maximum* at $c$ if $f(c) >= f(x)$. We call $f(c)$ the maximum value of $f$.
The absolute **maximum** is the largest possible output value for a function. The absolute **maximum** is the largest possible output value for a function.
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# Critical Numbers # Critical Numbers
A number is considered critical if the output of a function exists and $\dfrac{d}{dx}$ is zero or undefined. A number is considered critical if the output of a function exists and $\dfrac{d}{dx}$ is zero or undefined.
# Local Max/Min
A local max/min is a peak or trough at any point along the graph.