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Calculus Study Guide: Equations, Functions, and Rates of Change

Enhance your calculus skills with a detailed guide covering equations of lines, function properties, finding critical points, and analyzing rates of change. Master calculus concepts step-by-step!

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Calculus Study Guide: Equations, Functions, and Rates of Change

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  1. When you see… You think… Find the zeros

  2. To find the zeros...

  3. When you see… Find equation of the line tangent to f (x) at(a, b) You think…

  4. Equation of the tangent line

  5. When you see… Find equation of the line normal to f (x) at(a, b) You think…

  6. Equation of the normal line

  7. When you see… Show that f (x) is even You think…

  8. Even function

  9. When you see… Show that f (x) is odd You think…

  10. Odd function

  11. When you see… Find critical numbers You think…

  12. Find critical numbers

  13. When you see… Find the interval where f (x) is increasing You think…

  14. f (x) is increasing

  15. When you see… Find the interval where the slope of f (x) is increasing You think…

  16. Slope of f (x) is increasing

  17. When you see… Find the minimum value of a function You think…

  18. Minimum value of a function

  19. When you see… Find the minimum slope of a function You think…

  20. Minimum slope of a function

  21. When you see… Find inflection points You think…

  22. Find inflection points

  23. When you see… Show that exists You think…

  24. Show exists Show that

  25. When you see… Show that f (x) is continuous You think…

  26. f (x) is continuous at x = a

  27. When you see… Find vertical asymptotes of f (x) You think…

  28. Find vertical asymptotes of f (x)

  29. When you see… Find horizontal asymptotes of f (x) You think…

  30. Find horizontal asymptotes of f (x)

  31. When you see… Find the average rate of change of f (x) at[a, b] You think…

  32. Average rate of change of f (x)

  33. When you see… Find the instantaneous rate of change of f (x) at x=a You think…

  34. Instantaneous rate of change of f (x)

  35. When you see… You think…

  36. Average value of the function

  37. When you see… Find the absolute minimum of f (x) on[a, b] You think…

  38. Find the absolute minimum of f(x)

  39. When you see… Show that a piecewise function is differentiable at the point awhere the function rule splits You think…

  40. Show a piecewise function is differentiable at x=a

  41. When you see… Given s(t) (position function), findv(t) You think…

  42. Given position s (t), find v (t)

  43. When you see… Given v(t), find how far a particle travels on[a, b] You think…

  44. Given v (t), find how far a particle travels on [a,b]

  45. When you see… Find the average velocity of a particle on[a, b] You think…

  46. Find the average velocity on [a,b]

  47. When you see… Given v(t), determine if a particle is speeding up at t = k You think…

  48. Given v(t), determine if the particle is speeding up at t =k

  49. When you see… Given v(t) and s(0), find s(t) You think…

  50. Given v (t) and s(0), find s (t)

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