📍Local📍 vs. 🌎global🌎 extrema on an interval #apcalculus #apcalc #unit5 #shorts
We look at the difference between local and global extrema, also known as relative and absolute extrema, when we're considering an interval (a,b). For a function that's continuous over an interval from a to b, it's guaranteed that the function will achieve both its highest and lowest values at least once within this interval. This principle lays the foundation for identifying the extrema of functions in specified ranges.
We highlight how a function can have both a local maximum and minimum within an interval, marking the highest and lowest points in localized regions. However, it's crucial to note that when these points are compared with the interval's endpoints, the absolute extrema (the highest and lowest values in the entire interval) might be located at different points.
#APCalculus #CalculusConcepts #MathEducation #LocalVsGlobalExtrema #CalculusTips
Unit 5 of AP Calculus is all about Analytical Applications of Differentiation:
5.1 Using the Mean Value Theorem
5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
5.6 Determining Concavity of Functions over Their Domains
5.7 Using the Second Derivative Test to Determine Extrema
5.8 Sketching Graphs of Functions and Their Derivatives
5.9 Connecting a Function, Its First Derivative, and Its Second Derivative
5.10 Introduction to Optimization Problems
5.11 Solving Optimization Problems
5.12 Exploring Behaviors of Implicit Relations
_____
For extra help with your AP Calc (AB or BC), get my Ultimate Review Packet to help you review all year long and get prepared for the AP test:
AB: https://www.ultimatereviewpacket.com/courses/calculus-ab
BC: https://www.ultimatereviewpacket.com/courses/calculus-bc
Видео 📍Local📍 vs. 🌎global🌎 extrema on an interval #apcalculus #apcalc #unit5 #shorts канала Krista King
We highlight how a function can have both a local maximum and minimum within an interval, marking the highest and lowest points in localized regions. However, it's crucial to note that when these points are compared with the interval's endpoints, the absolute extrema (the highest and lowest values in the entire interval) might be located at different points.
#APCalculus #CalculusConcepts #MathEducation #LocalVsGlobalExtrema #CalculusTips
Unit 5 of AP Calculus is all about Analytical Applications of Differentiation:
5.1 Using the Mean Value Theorem
5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
5.6 Determining Concavity of Functions over Their Domains
5.7 Using the Second Derivative Test to Determine Extrema
5.8 Sketching Graphs of Functions and Their Derivatives
5.9 Connecting a Function, Its First Derivative, and Its Second Derivative
5.10 Introduction to Optimization Problems
5.11 Solving Optimization Problems
5.12 Exploring Behaviors of Implicit Relations
_____
For extra help with your AP Calc (AB or BC), get my Ultimate Review Packet to help you review all year long and get prepared for the AP test:
AB: https://www.ultimatereviewpacket.com/courses/calculus-ab
BC: https://www.ultimatereviewpacket.com/courses/calculus-bc
Видео 📍Local📍 vs. 🌎global🌎 extrema on an interval #apcalculus #apcalc #unit5 #shorts канала Krista King
Показать
Комментарии отсутствуют
Информация о видео
Другие видео канала
![Cardiac output - simpson's rule (KristaKingMath)](https://i.ytimg.com/vi/ssr-IINl-Ec/default.jpg)
![Step-by-step 👟👟 for the Second Derivative Test 🤓 #apcalculus #apcalc #unit5 #shorts](https://i.ytimg.com/vi/sjR8xeqVmco/default.jpg)
![Parabolas -Vertex, Axis, Focus, Directrix (KristaKingMath)](https://i.ytimg.com/vi/IHSQ6Qzyziw/default.jpg)
![📏Distance traveled📏 🟰 〰️Arc length〰️ #apcalculus #apcalc #unit8 #shorts](https://i.ytimg.com/vi/L76ysBbDteg/default.jpg)
![Long Division of Polynomials Example 1 (KristaKingMath)](https://i.ytimg.com/vi/wC_t2frlO9A/default.jpg)
![❌NEVER❌ choose the wrong 〰️arc length〰️ formula 🥵 #apcalculus #apcalc #unit8 #shorts](https://i.ytimg.com/vi/Z1TxBWu2gW8/default.jpg)
![Polar Parametric Curve - Arc Length (KristaKingMath)](https://i.ytimg.com/vi/pwxO2zpI8Kw/default.jpg)
![30-60-90 triangles (KristaKingMath)](https://i.ytimg.com/vi/L_BBP2QQz38/default.jpg)
![Differentiate ↗️vector-valued↗️ functions, BUT MAKE IT EASY 😅😅 #apcalculus #apcalc #unit9 #shorts](https://i.ytimg.com/vi/NyegIj00mIw/default.jpg)
![Implicit differentiation for ⬅️BOTH SIDES➡️ of the equation 🤔 #apcalculus #apcalc #unit3 #shorts](https://i.ytimg.com/vi/d0jmkbYuu_g/default.jpg)
![Rapid calculus - derivatives of inverse trig functions - arccos (KristaKingMath)](https://i.ytimg.com/vi/WOs1QCn2mjM/default.jpg)
![🕵️♀️Investigating 👆increasing/decreasing👇 behavior #apcalculus #apcalc #unit5 #shorts](https://i.ytimg.com/vi/Qj6WL5tIEcI/default.jpg)
![Candidates Test for 🧨EXTREMA🧨! 😎😎 #apcalculus #apcalc #unit5 #shorts](https://i.ytimg.com/vi/sy6yiXxEdHU/default.jpg)
![SALES DECLINE calculus problems (KristaKingMath)](https://i.ytimg.com/vi/Yvup-dHJxIM/default.jpg)
![Rapid calculus - equation of the normal line (KristaKingMath)](https://i.ytimg.com/vi/cAUzvRgAurI/default.jpg)
![direct variation (KristaKingMath)](https://i.ytimg.com/vi/itnZ8hkBSkc/default.jpg)
![Limits algebraically🔡, from a table🗒️, from the graph📉 #apcalculus #apcalc #unit1 #shorts](https://i.ytimg.com/vi/MXjgW_7NShE/default.jpg)
![Finding 🦁carrying capacity🦁 from a logistic equation ✏️✏️ #apcalculus #apcalc #unit7 #shorts](https://i.ytimg.com/vi/rmW9bpobxkk/default.jpg)
![The nth term test 🚨ONLY🚨 determines divergence! 🤓 #apcalculus #apcalc #unit10 #shorts](https://i.ytimg.com/vi/YtF1BtVYytQ/default.jpg)
![How solution curves are ⛓️BOUNDED⛓️ in a direction field #apcalculus #apcalc #unit7 #shorts](https://i.ytimg.com/vi/TRfDbEOsH_I/default.jpg)
![How to 🏃💨 QUICKLY set up Riemann sum approximations 📶 #apcalculus #apcalc #unit6 #shorts](https://i.ytimg.com/vi/zoBDglxqMqY/default.jpg)