How to Think About and Solve Related Rates Problems in Calculus

Related rates problem in calculus are hard. But you can improve by working through many example problems and solutions. Problem types: 1) Rate of change of atmospheric pressure for an airplane based on altitude and rate of ascent. 2) Rate of change of diagonal of a rectangle based on the side lengths and the rate of change of a side length (use Pythagorean Theorem). 3) Rate of change of distance between two cars with the Pythagorean Theorem. 4) Based on rate of rotation (in radians per second), find the rate of a change of where a beam of light from a lighthouse hits the shoreline (trigonometry is needed). 5) Coffee filter emptying of water (cone shape — similar triangles are needed). Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb.

🔴 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 #RelatedRates #ProblemSolving

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(0:00) How fast is atmospheric pressure decreasing as a plane ascends?
(9:38) How fast is the diagonal of a rectangle changing when one side is changing at a certain rate?
(17:31) How fast is the distance between two cars changing when one is traveling east and one is traveling north (at different rates)?
(24:40) How fast is a spot of light moving as a lighthouse beam of light rotates?
(31:29) How fast is the water level falling in a cylindrical cone (coffee filter) when the rate of change of the volume is constant?

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