In this video we will learn the FUNDAMENTALS OF OPTIMIZATION with DERIVATIVES. We will talk about how the derivative helps us understand the increasing or decreasing behavior of a function and how this allows us to find the maximum or minimum points of a FUNCTION. Through an example we will see how THE FIRST DERIVATIVE is used to FIND THE MAXIMUM OR MINIMUM. In addition, we will see how THE SECOND DERIVATIVE gives us information about the INFLECTION POINT and how this also allows us to find MAXIMUM AND MINIMUM OF A FUNCTION. The creation of these videos takes me quite a bit of time. If you want to help me continue creating content on YouTube, I invite you to support me on PATREON and ACCESS EXCLUSIVE BENEFITS: / bluedot96 #calculation #multivariablecalculation #optimization CHAPTERS: 00:00 Introduction 00:20 What is optimization? 01:32 Growth and decrease of a function 02:50 Global maximum of a function 03:42 Global minimum of a function 04:36 Local or relative maxima and minima 06:27 The derivative and the growth or decrease of a function 07:46 Derivative at maximum or minimum points 09:53 Criterion of the first derivative 10:26 Maxima and minima of f(x) = x^3-3x+2 15:46 Analysis of the graphs of the function and its derivative 16:29 There are not always maxima or minima at f'(x) = 0 19:02 Maxima and minima at points where the derivative does not exist? 20:04 Criterion of the second derivative 23:39 Conclusions and farewell The creation of these videos takes me quite a bit of time. If you want to help me continue creating content on YouTube, I invite you to support me on PATREON and ACCESS EXCLUSIVE BENEFITS: / bluedot96 Follow me on Twitter: / bluedot96 Follow me on Facebook: / bluedot1196 Follow me on Instagram: / pauloch96 I RECOMMEND THESE VIDEOS: WHAT IS THE DERIVATIVE?: • The DERIVATIVE changed EVERYTHING ???? WHAT is... WHAT IS THE INTEGRAL?: • What is the INTEGRAL? MEANING of... WHAT IS A FUNCTION?: • A function is NOT A MACHINE WHAT... FUNCTIONS FROM SCRATCH: • WHAT is A FUNCTION? ▶ CART PRODUCT... LINEAR FUNCTION: • What is a LINEAR FUNCTION? ▶ GRAPH... QUADRATIC FUNCTION: • WHAT is a QUADRATIC FUNCTION? ▶ Com... FUNCTIONS OF TWO VARIABLES: • WHAT is A FUNCTION OF TWO VARIABLES?... THE INTEGRAL FROM SCRATCH: • This THEOREM CHANGED EVERYTHING ???? WHAT... DIFFERENTIATION : • This IDEA OF NEWTON FOUNDED the BASIS... RULES OF DERIVATION: • The UNKNOWN side of the DERIVATIVE ????... WHAT IS CALCULUS?: • Why did CALCULUS CHANGED EVERYTHING? ... WHAT IS A LIMIT?: • A FANTASTIC INTRODUCTION to LIMITS... THE LIMIT EXPLAINED IN DETAIL: • WHAT is the LIMIT of a FUNCTION? ▶OF... LIMIT PROPERTIES: • WHAT IS behind the FAMOUS PROPERTIES... WHAT IS OPTIMIZE?: • Why SHOULD YOU LEARN OPTIMIZATION... WHERE DO SIN, COS AND TAN COME FROM?: • REALLY UNDERSTANDING WHAT SIN, COS... UNDERSTANDING SIN, COS AND TAN: • UNDERSTANDING the SIN, COS AND TAN FUNCTIONS You can support the making of more videos of this style by being a MEMBER OF THE CHANNEL, with your help I will be able to make more videos until I complete a playlist with university mathematics from the most basic to the most complex through animations! ************************************************************************************************* The animations in this video were made with Manim (Mathematical animation), a library for Python created by Grant Sanderson (3Blue1Brown). Personally, I find it a very useful tool to better explain many concepts in a visual way. If you are interested, here is the link to the Manim library for Python: https://github.com/3b1b/manim VIDEOS: PEXELS Without further ado, thank you for your attention and see you in the next video