Applications of Differentiation

Explore the practical applications of differentiation in this comprehensive 2-hour 30-minute video lecture. Delve into key concepts such as the Extreme Value Theorem, First and Second Derivative Tests, and concavity. Learn techniques for sketching graphs of rational and polynomial functions. Master L'Hospital's Rule for various indeterminate forms. Tackle optimization problems, including finding the closest point, largest rectangle in a semicircle, largest box, and largest cone cup. Apply related rates to real-world scenarios like ripples in a pond, driving to meet a friend, and walking away from a lamppost. Enhance your understanding of calculus and its real-world applications through this in-depth exploration of differentiation techniques.

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.