1. What makes a function continuous?
    A limit exists for all f(x) approaching a and the lim at f(x) = f(a)
  2. Are all polynomial functions continuous?
  3. What are the local min and max?
    Points where f prime evaluates to zero (ie No slope bc at bottom of pit)
  4. What is the derivative of 1 - x?
  5. What is the derivative of -5 + 11 - 6x?
  6. What is the derivative of x/40?
  7. What is the integral of 1/sqrt(x)?
    2 sqrt(x)
  8. How many feet in a mile?
  9. What is the extreme value theorem?
    if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain its maximum and minimum value, each at least once.
  10. Can a function have no maximum and minimum values?
    Yes, x3 is an example
  11. What is Fermat's Theorem?
    If f has a local max or min at c, and if f'(c) exists, then f'(c) = 0.
  12. What is a critical number?
    A number c in the domain of f such that either f'(c) = 0 or f'(c) does not exist.
  13. Is the local min or max always a critical number?
  14. What is the closed interval method? (to find absolute max/min)
    • 1. Find values of f at critical points.
    • 2. Find values of f at end points.
    • 3. Largest/smallest wins.
  15. What is the Mean Value Theorem?
    f(b) - f(a) = f'(c)(b-a) At a point(s) the tangent line is parallel to the secant line.
  16. When is a function increasing?
    f'(x) > 0
  17. When is a function decreasing?
    f'(x) < 0
  18. What is the First Derivative test?
    • A. (f' + to - at c) = (f has loc max at c)
    • B. (f' - to + at c) = (f has loc min at c)
    • C. (f' stays the same at c) = (f does not have min/max at c)
  19. If f' is increasing on I what does concavity look like?
    Concave up :)
  20. If f' is decreasing on I what does concavity look like?
    Concave down :(
  21. What is an inflection point?
    Point where curve switches concavity
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