diff --git a/.obsidian/plugins/obsidian-git/data.json b/.obsidian/plugins/obsidian-git/data.json index e69de29..bef4c6e 100644 --- a/.obsidian/plugins/obsidian-git/data.json +++ b/.obsidian/plugins/obsidian-git/data.json @@ -0,0 +1,27 @@ +{ + "commitMessage": "vault backup: {{date}}", + "autoCommitMessage": "vault backup: {{date}}", + "commitDateFormat": "YYYY-MM-DD HH:mm:ss", + "autoSaveInterval": 5, + "autoPushInterval": 0, + "autoPullInterval": 5, + "autoPullOnBoot": true, + "disablePush": false, + "pullBeforePush": true, + "disablePopups": false, + "listChangedFilesInMessageBody": false, + "showStatusBar": true, + "updateSubmodules": false, + "syncMethod": "merge", + "customMessageOnAutoBackup": false, + "autoBackupAfterFileChange": false, + "treeStructure": false, + "refreshSourceControl": true, + "basePath": "", + "differentIntervalCommitAndPush": false, + "changedFilesInStatusBar": false, + "showedMobileNotice": true, + "refreshSourceControlTimer": 7000, + "showBranchStatusBar": true, + "setLastSaveToLastCommit": false +} \ No newline at end of file diff --git a/education/math/MATH1210 (calc 1)/Max and Min.md b/education/math/MATH1210 (calc 1)/Max and Min.md index bc8c261..1c834c4 100644 --- a/education/math/MATH1210 (calc 1)/Max and Min.md +++ b/education/math/MATH1210 (calc 1)/Max and Min.md @@ -11,4 +11,14 @@ The absolute **minimum** is the smallest possible output value for a function. 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. \ No newline at end of file +A local max/min is a peak or trough at any point along the graph. + +# Extreme Value Theorem +If $f$ is a continuous function in a closed interval $[a, b]$, then $f$ achieves both an absolute maximum and an absolute minimum in $[a, b]$. Furthermore, the absolute extrema occur at $a$ or at $b$ or at a critical number between $a$ and $b$. + +## Example +> Find the absolute maximum and absolute minimum of the function $f(x) = x^2 -3x + 2$ on the closed interval $[0, 2]$: +1. $x=0$ and $x=2$ are both critical numbers because they are endpoints. Endpoints are *always* critical numbers because $\dfrac{d}{dx}$ is undefined. +2. $\dfrac{d}{dx} x^2 -3x + 2 = 2x -3$ +3. Setting the derivative to zero, $0 = 2x - 3$ +4. Solving for x, we get $x = \dfrac{3}{2}$. Three halves is a critical number because $ \ No newline at end of file