Master Applications of Derivatives

Learn everything from Applications of Derivatives, then test your knowledge with 180+ practice questions

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“I’m currently taking an 8 week, summer Calc 1 course and this online course is a good way to help reinforce the topics discussed in class. Everything is presented in a clear manner and is easy to understand.”

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Course Summary

Learn everything you need to know to get through the end of Calc 1 and prepare you to go into Calc 2 with a solid understanding of what’s going on. Video explanations, text notes, and quiz questions that won’t affect your class grade help you “get it” in a way most textbooks never explain.

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Course outline

The curriculum includes:

Optimization
- Critical points
- Increasing and decreasing, and first derivative test
- Concavity, and second derivative test
Sketching graphs
- Vertical asymptotes, horizontal asymptotes, slant asymptotes
- Sketching graphs
- Extrema on a closed interval
- Sketching f(x) given the graph of f'(x), or vice versa
Linear approximation
- Linear approximation
- Linear approximation to estimate a root
- Linearization
Related rates
- Radius of the balloon
- Price of the product
- Water level in the tank
- Observer and the airplane
- Ladder sliding down the wall
Applied optimization
- Dimensions of a rectangle that maximize its area
- Dimensions of a rectangle that minimize its perimeter
- Dimensions that minimize page size with a given printed area
- Two real numbers with minimum product
- Two real numbers with minimum sum of squares
- Point on the line closest to another point
- Time when velocity is minimum
- Dimensions that maximize the volume of a box
- The open top box
- Dimensions that minimize the surface area of an open top box
- Width that minimizes the surface area of an open top box
- Dimensions that maximize the volume of a cylinder
- Dimensions that minimize the surface area of a cylinder
- Maximum volume of a cone shaped cup
- Production level and sale price that maximize profit
- Sales level that maximizes revenue
- Maximum area of a rectangle inscribed in a semicircle
- Dimensions that maximize the area of a rectangle inscribed in a triangle
- Maximum volume of a cylinder inscribed in a sphere

Derivative theorems
- Mean value theorem for derivatives
- Rolle's theorem
- Newton's method
- L'Hospital's rule
Physics
- Position function
- Particle motion
- Instantaneous velocity
- Vertical motion
- Ball thrown up from the ground
- Coin dropped from the roof
Economics
- Marginal cost, revenue and profit
Exponential growth and decay
- Half life
- Compounding interest
- Sales decline