TOC
Courses
Blog
Twitch
Shop
Search

Courses
Blog
Subreddit
Discord
Log in
Sign up

▾Calculus 1
- ▸Limits and continuity
  - •Intro to calc 1
  - •Estimating limits from graphs
  - •Estimating limits from tables
  - •Intro to continuity
  - •Finding and classifying discontinuities
  - •Finding the value that makes the function continuous
- ▸Derivatives: definition and basic derivative rules
  - •Proving differentiable implies continuous
  - •Derivative of a function from first principles
  - •Finding the tangent or normal line through the given point
  - •Constant rule
  - •Constant multiple rule for derivatives
  - •Sum, difference, and power rules for derivatives
  - •Product rule
  - •Proving the product rule
  - •Quotient rule
  - •Derivatives of trig functions
  - •Proving properties of even and odd functions (calculus 1)
  - •Leibniz's derivative notation
  - •Logarithmic functions
- ▸Derivatives: composite, implicit, and inverse functions
  - •Derivative at a point from first principles
  - •Derivatives of exponential functions
  - •Derivatives of logarithmic functions
  - ▸Derivatives of hyperbolic and inverse hyperbolic functions
    - •Using the derivatives of the hyperbolic functions
    - •Proving the derivatives of the hyperbolic functions
    - •Proving the derivatives of the inverse hyperbolic functions
  - •Derivatives of inverse trig functions
  - •Derivatives of transcendental functions
  - •Derivatives of trigonometric functions under transformations
  - •Derivative using u-substitution
  - •Determining derivatives from graphs
  - •Higher order derivatives
  - •Chain rule
  - •Derivatives of inverse functions
  - •Choosing the derivative rules to use
- ▾Applying derivatives to analyze functions
  - •Applications of trigonometric derivatives
  - •Extreme value theorem
  - •First derivative test
  - •Mean value theorem
  - ▸Monotonic intervals and functions
    - •Intro
    - •Proofs
  - •Related rates
  - •Second derivative test
  - •Concavity
  - •Factoring a cubic polynomial with a double root
  - •Graphing using derivatives
  - ▸Special points
    - ▸Finding critical values from graphs
      - •Lesson
      - •Practice
    - •Finding critical values using derivatives
    - ▸Inflection points
      - •Graphically finding points of inflection
      - •Using the second derivative to find points of inflection
    - •Classifying stationary points
    - •Sketching polynomials using stationary points
  - •Bisection method
  - •Newton's method
  - •False position method
  - •L'Hopital's rule
- ▸Integrals
  - •Basic integration problems
  - ▸Integration by u-substitution
    - ▸Integration by u-substitution (less difficult)
      - •Lesson
      - •Practice
    - •Integration by u-substitution (more difficult)
    - •Integrating exponential functions by u-substitution
  - •Visually determining antiderivative
- ▸Applications of integrals
  - •Proving the formula for the area of a circle
  - •Area between two curves
  - ▸Solids of revolution
    - •Disc and washer methods (circular cross sections)
    - •Volumes of solids with known cross sections
    - •Shell method
    - •Volume of a sphere (calculus \(2\))
    - •Volume of a cone (calculus 2)

› Calculus 1 › Applying derivatives to analyze functions

Special points

Finding critical values from graphs
Finding critical values using derivatives
Inflection points
Classifying stationary points
Sketching polynomials using stationary points
Other resources

Conclude by giving your students these challenges:

Phew I'm Factored by NRICH
You Can't Make an Omelette... by NRICH
2002 AMC 8, Problem 1

Mentally determine what fraction is shaded.

Answer: \((1/4)\pi - 1/4\)