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education/math/MATH1210 (calc 1)/Max and Min.md
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# Absolute Maximum # Absolute 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.
# Absolute Minimum
A function $f$ has an absolute minimum at $c$ if $f(c) <= f(x)$. $f(c)$ is the absolute minimum value of $f$. A function $f$ has an absolute minimum at $c$ if $f(c) <= f(x)$. $f(c)$ is the absolute minimum value of $f$.
The absolute **minimum** is the smallest possible output value for a function.
The absolute minimum is the smallest possible output value for a function. - Where the derivative of a function is zero, there is either a peak or a trough.