How to Find Local Maximum and Minimum Values of a Rational Function | Calculus | Glass of Numbers

In this video, we use the First Derivative Test to find the local maximum and minimum values of a rational function. How to find the local extreme values? We first need to find critical numbers of the function. Then plot the critical numbers on the number line (x-axis) to construct a sign analysis chart. This chart will tell us on what interval the function is increasing or decreasing. We can next apply the First Derivative Test to find the local maximum and minimum values. Note that because we are finding the max and min values, we will finding the y-values of the function. Do not confuse this with the location of the extrema, which are the x-values. See here how to find the local extreme values for a polynomial function:    • How to Find Local Maximum and Minimum Valu...   See here how to deal with a trigonometric function with infinitely many local max and min:    • How to Find Local Maximum and Minimum Valu...   See here how to find the local extreme values for a sum of exponential function:    • How to Find Local Maximum and Minimum Valu...   📺 Subscribe to my channel for Math Learning! https://www.youtube.com/glassofnumber... Please help me by subscribing to my YouTube channel. I want to use my free time to make a lot of math videos to help others and to make education available to the world. Your sharing and subscribing will help this channel be reached by more people. Thank you! Follow me:   / glassofnumbers   https://www.glassofnumbers.com Ayúdame suscribiéndome a mi canal de YouTube. Quiero usar mi tiempo libre para hacer muchos videos de matemáticas para ayudar a otros y hacer que la educación esté disponible para el mundo. Tus Me gusta y Suscripciones ayudarán a que más personas lleguen a este canal. ¡Gracias! 請訂閱我的YouTube Channel, 我會製作更多與數學相關的視頻，讓世界各地的朋友用簡單的方法學習數學（數學考試一定A）！請用您的訂閱和點贊支持我，並在留言區與我討論！謝謝！ #Calculus #LocalExtrema #CurveSketching