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When you see…

When you see…. You think…. Find the zeros. To find the zeros. When you see…. Find equation of the line tangent to f ( x ) at [a,b]. You think…. Equation of the tangent line. When you see…. Find equation of the line normal to f ( x ) at [ a , b ]. You think….

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When you see…

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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… Find the interval where f(x) is increasing You think…

  8. f(x) increasing

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

  10. Slope of f (x) is increasing

  11. When you see… Find the minimum value of a function (open interval) You think…

  12. Minimum value of a function

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

  14. Find critical numbers

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

  16. Find inflection points

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

  18. Show exists Show that the limit from the left is equal to the limit from the right

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

  20. .f(x) is continuous

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

  22. Find vertical asymptotes of f(x) Then x=c is a vertical asymptote To find VA of a rational function: • Factor and reduce f(x) • Set denominator = 0 • VA are x-values where the den = 0

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

  24. Find horizontal asymptotes of f(x)

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

  26. Average rate of change of f(x)THINK: Derivative Find

  27. When you see… Find the instantaneous rate of change of f(x) on[a, b] You think…

  28. Instantaneous rate of change of f(x)THINK: Derivative at a point Find f’( a)

  29. When you see… You think…

  30. Average value of the function

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

  32. Find the absolute minimum of f(x)on a closed interval

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

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

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

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

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

  38. Given v(t), find how far a particle travels on [a,b]Total Distance Traveled

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

  40. Think: Find the average rate of change on [a,b] - SLOPE

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

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

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

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

  45. When you see… Show that Rolle’s Theorem holds on[a, b] You think…

  46. Show that Rolle’s Theorem holds on [a,b]

  47. When you see… Show that the Mean Value Theorem holds on[a, b] You think…

  48. Show that the MVT holds on [a,b]

  49. When you see… Find f ’(x) by definition You think…

  50. Find f ‘( x) by definition

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