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AP CALCULUS BC - Coggle Diagram

- - - - Comparison test
      - Ratio test
      - Root test
      - Integral test
      - Limit comparison test
      - Limit comparison test
- - - - Differentiation can be applied to measure the function per unit change in the independent variable.
  - - - The intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval.
    - - The theorem states that if f is a continuous function on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in (a,b) such that the tangent at c is parallel to the secant line through the endpoints （a,f(a) ）and b,f(b) ）
    - - The extreme value theorem states that if a real-valued function f is continuous on the closed interval [a,b], then f must attain a maximum and a minimum, each at least once.
- - - - the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two
- - - - for Infinite Limit
      - for Discontinuity
- - - - Velocity is rate of change in position, so its definite integral will give us the displacement of the moving object.
      - Speed is the rate of change in total distance, so its definite integral will give us the total distance covered, regardless of position.
- - - - EG
  - - - a statistical measure of the strength of the relationship between the relative movements of two variables