Скачать или смотреть The Derivative at a Point (Calculus Problems and Solutions)

Use the limit definition of the derivative to find the derivative f(x)=x^2 at x=2, f(x)=1/x^2=x^-2 at x=-1, and f(x)=sqrt(x)=x^1/2 (square root) at x = 4 (use a difference quotient in each case). Interpret the derivative as the slope of a tangent line and rate of change. Use linear approximation to estimate a function value. Estimate the derivative of atmospheric pressure with respect to altitude. 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 #derivatives #calculusderivatives

Links and resources
===============================
🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn...
🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/
🔴 Follow me on Twitter:   / billkinneymath  
🔴 Follow me on Instagram:   / billkinneymath  
🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA.
🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/

(0:00) Use a limit to find f'(2) when f(x)=x^3 (limit definition of the derivative, the limit of a difference quotient).
(6:24) Use a limit to find f'(-1) when f(x)=1/x^2
(9:54) Use a limit to find f'(4) when f(x)=x^1/2=sqrt(x)
(12:49) Find the tangent line at x=10 when f(10)=5 and f'(10)=2
(17:57) Tangent line approximation of f(x)
(21:08) Fill in the blanks about f and f' when given a tangent line
(22:41) Geometric interpretations of function values and derivative values
(28:39) Atmospheric pressure application (interpret the derivative)


AMAZON ASSOCIATE
As an Amazon Associate I earn from qualifying purchases.