Finding Local Maxima and Minima of a Function by Differentiation (First and Second Derivative Tests)

Solve problems about how to use the first and second derivative to find and classify critical points of a function as local maxima, local minima, or neither. Inflection points are also found. Symbolic and graphical problems. Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb.

The First Derivative Test classifies a critical point of a function based on the behavior of the first derivative of the function near the critical point, while the Second Derivative Test does so based on the behavior of the second derivative of the function near the critical point.

🔴 Calculus 1, Lesson 1.1: Linear Functions (3Blue1Brown SoME2): https://www.youtube.com/watch?v=lmCjnxzIals

🔴 Calculus 1, Lesson 1.2: Exponential Functions: https://www.youtube.com/watch?v=47ZqW19AjD4

🔴 Calculus 1, Lesson 1.3: Quadratic Functions, Transformations of Functions, and Function Composition: https://www.youtube.com/watch?v=1T58CnSME4g

🔴 Calculus 1, Lesson 1.4: Logarithmic Functions (Intro to Horizontal Compressions & Inverse Functions): https://www.youtube.com/watch?v=oS-gvIoJf60

🔴 Calculus 1, Lesson 1.5: Trigonometric Functions and Inverse Trigonometric Functions: https://www.youtube.com/watch?v=UFYjlnGUenE

🔴 AP Calculus AB Exam Review: Practice Exam Problems & Solutions (Multiple Choice, No Calculator): https://www.youtube.com/watch?v=2AG_Dt3x7q0

🔴 AP Calculus AB Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=RLgUwP44V_M

🔴 AP Calculus BC Exam Review: Practice Exam (30 Question Multiple Choice, No Calculator): https://www.youtube.com/watch?v=1Q7ALcwT97A

🔴 AP Calculus BC Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=ZWisJEDP44w

🔴 Calculus 1 Exam 1 Review Problems and Solutions (Precalculus, Limits, Continuity, Derivatives): https://www.youtube.com/watch?v=UjmvUwvd7c4

🔴 Calculus 1 Course, Lecture 1: The Big Ideas (Rates & Areas, the Infinity Principle & Circular Area): https://www.youtube.com/watch?v=2V_ehJC5QUY

🔴 Calculus 1 Course Lecture Playlist: https://www.youtube.com/playlist?list=PLmU0FIlJY-MkFrKtM0S0NLu-TxZa5jBIx

#calculus #optimization #CriticalPoint

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(0:00) Cubic example: f(x)=x^3-9x^2+24x-5
(6:32) Quintic (5th degree) example: f(x)=x^5-10x^3-8
(13:26) f(x)=4x-2ln(x)
(17:01) f(x)=x*e^(-2x)
(20:54) f(x)=sin(x)+cos(x) (infinitely many critical points)
(27:29) f(x)=x^3-a*x (parameterized family of functions in the parameter “a”)
(33:00) Given graph of derivative f’, mark local maxima, local minima, and inflection points
(38:47) Given 3 graphs, decide which is f, which is f’, and which is f”

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