Function Families are Family Fun! 😀 (Calculus Problems and Solutions)

Описание: How does the graph of a function change as a parameter changes? Derivatives in Calculus help us analyze this interesting math subject. We find critical points and inflection points for various families of functions, based on one or two parameters. Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb.

🔴 Calculus 1, Lesson 1.1: Linear Functions (3Blue1Brown SoME2):    • Calculus 1, Lesson 1.2: Exponential Functions  

🔴 Calculus 1, Lesson 1.2: Exponential Functions:    • Calculus 1, Lesson 1.1: Linear Functions (...  

🔴 Calculus 1, Lesson 1.3: Quadratic Functions, Transformations of Functions, and Function Composition:    • Calculus 1, Lesson 1.3: Quadratic Function...  

🔴 Calculus 1, Lesson 1.4: Logarithmic Functions (Intro to Horizontal Compressions & Inverse Functions):    • Calculus 1, Lesson 1.4: Logarithmic Functi...  

🔴 Calculus 1, Lesson 1.5: Trigonometric Functions and Inverse Trigonometric Functions:    • Calculus 1, Lesson 1.5: Trigonometric Func...  

🔴 AP Calculus AB Exam Review: Practice Exam Problems & Solutions (Multiple Choice, No Calculator):    • AP Calculus AB Exam Review 2025: Practice ...  

🔴 AP Calculus AB Exam Review: Free Response Practice Exam Problems & Solutions:    • AP Calculus AB Exam Review 2025: Free Resp...  

🔴 AP Calculus BC Exam Review: Practice Exam (30 Question Multiple Choice, No Calculator):    • AP Calculus BC Exam Review 2025: Practice ...  

🔴 AP Calculus BC Exam Review: Free Response Practice Exam Problems & Solutions:    • AP Calculus BC Exam Review 2025: Free Resp...  

🔴 Calculus 1 Exam 1 Review Problems and Solutions (Precalculus, Limits, Continuity, Derivatives):    • Calculus 1 Exam 1 Review Problems and Solu...  

🔴 Calculus 1 Course, Lecture 1: The Big Ideas (Rates & Areas, the Infinity Principle & Circular Area):    • Calculus 1 Course, Lecture 1: The Big Idea...  

🔴 Calculus 1 Course Lecture Playlist:    • Calculus 1 Course Lectures  

#calculus #CalculusDerivatives #Mathematica

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(0:00) f(x)=x^3+a*x. How do the critical points and inflection points change as the parameter "a" changes? How does the graph change?
(7:28) f(x)=x^2+a/x. How do the critical points and inflection points change as the parameter "a" changes? How does the graph change?
(17:07) f(x)=a*x*e^(-b*x). How do the critical points and inflection points change as the parameters "a" and "b" change? How does the graph change?
(26:51) f(x)=e^(-a*x)*sin(b*x). How do the critical points change as the parameters "a" and "b" change? How does the graph change?


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