Math 22 Extrema and First Derivative Test

Relative Extrema

 Let $f$ be a function defined at $c$.
 1. $f(c)$ is a relative maximum of $f$ when there exists an interval Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (a,b)}
 containing $c$ such that $f(x)\leq f(c)$ for all $x$ in $(a,b)$.
 2. $f(c)$ is a relative minimum of $f$ when there exists an interval $(a,b)$ containing $c$ such that $f(x)\geq f(c)$ for all $x$ in $(a,b)$.

If $f$ has a relative minimum or relative maximum at $x=c$, then $c$ is a critical number of $f$. That is, either $f'(c)=0$ or $f'(c)$ is undefined.

Relative extrema must occur at critical numbers as shown in picture below.

Absolute Extrema

The page is under Construction

Return to Topics Page

This page were made by Tri Phan