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▾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 from graphs: Practice

YouTube videos

80680Screencast 3.1.3: Identifying critical values graphically
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