Calculus - Graphing

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Calculus

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7 Terms

1
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second derivative

gives the concavity

  • measures the change in slope

2
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second deriv > 0

  • positive

  • concave up

<ul><li><p>positive</p></li><li><p>concave up</p></li></ul>
3
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second deriv < 0

  • negative

  • concave down

<ul><li><p>negative </p></li><li><p>concave down</p></li></ul>
4
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inflection pt

pt on curve when the curve changes from CU to CD and vice versa

5
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second deriv test

if f’(x) = 0 and f’’(x) > 0, there is a local MIN at x

if f’(x) = 0 and f’’(x) < 0, there is a local MAX at x

if f’’(x) = 0, then evaluate using intervals of decrease and increase

6
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all components of curve sketching

  • x-intercepts

  • y-intercepts (evaluate after x-intercepts bc it could be (0,0)

  • local max and mins from first deriv and the second deriv test

  • det concavity from second deriv by finding inf pts

7
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curve sketching for rational functions

same components as other graphs except you also need:

  • vertical asymptotes

  • horizontal asymptotes (LC’s if same deg top and bottom, y = 0 if deg on bottom is higher than deg on top, slant asymptote if deg on top is one higher than bottom)