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Applications of Differentiation

Math at Andrews via YouTube

Overview

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Learn to find extrema of functions, apply the Extreme Value Theorem, use the First and Second Derivative Tests, sketch rational and polynomial functions, apply L'Hospital's Rule in various indeterminate forms, optimize problems involving points, rectangles, boxes, and cones, and solve related rates problems like ripples in a pond, meeting a friend, and walking away from a lamppost. The course teaches differentiation applications through real-world scenarios and mathematical problem-solving techniques, making it suitable for learners interested in advanced calculus concepts and their practical applications.

Syllabus

Extrema of Function.
Extreme Value Theorem.
First Derivative Test.
Second Derivative and Concavity.
Sketching Graph of Rational Function.
Sketching the Graph of a Polynomial.
L'Hospital's Rule: Zero Over Zero?.
L'Hospital's Rule: Infinity Over Infinity?.
L'Hospital's Rule: Zero To The Zero?.
L'Hospital's Rule: Infinity Minus Infinity?.
Optimization: Closest Point.
Optimization: Largest Rectangle in Semicircle.
Optimization: Largest Box.
Optimization: Largest Cone Cup.
Related Rates: Ripples in a Pond.
Related Rates: Driving to Meet a Friend.
Related Rates: Walking Away from a Lamppost.

Taught by

math at andrews

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