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Sketching Functions

Sketching Functions. We are now going to use the concepts in the previous sections to sketch a function, find all max and min ( relative and absolute ), and identify any inflection points. Sketching Functions.

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Sketching Functions

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  1. Sketching Functions We are now going to use the concepts in the previous sections to sketch a function, find all max and min ( relative and absolute ), and identify any inflection points.

  2. Sketching Functions We are now going to use the concepts in the previous sections to sketch a function, find all max and min ( relative and absolute ), and identify any inflection points. Absolute maximum – a relative maximum with the highest value within a given interval Absolute minimum – a relative minimum with the lowest value within a given interval

  3. Sketching Functions

  4. Sketching Functions 1. Get your critical point(s) and find increasing decreasing.

  5. Sketching Functions 1. Get your critical point(s) and find increasing decreasing.

  6. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. decreasing increasing

  7. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. decreasing increasing

  8. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. Rel. max Rel. max Rel. min decreasing increasing

  9. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. Rel. max Rel. max Rel. min Absolute min This is the smallest relative min value… decreasing increasing

  10. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. 4. Identify any inflection point(s) and also find concave up/down. Rel. max Rel. max Rel. min Absolute min decreasing increasing

  11. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. 4. Identify any inflection point(s) and also find concave up/down. CU Rel. max Rel. max Rel. min Absolute min decreasing increasing Concave up If a derivative is equal to a constant, all input values will equal that constant…

  12. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. 4. Identify any inflection point(s) and also find concave up/down. CU CU Rel. max Rel. max Rel. min Absolute min decreasing increasing Concave up Concave up

  13. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. 4. Identify any inflection point(s) and also find concave up/down. 5. Sketch the graph CU CU Rel. max Rel. max Rel. min 5 Absolute min 5

  14. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. 4. Identify any inflection point(s) and also find concave up/down. 5. Sketch the graph

  15. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. 4. Identify any inflection point(s) and also find concave up/down. 5. Sketch the graph increasing decreasing increasing

  16. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. 4. Identify any inflection point(s) and also find concave up/down. 5. Sketch the graph Rel. max Rel. min Rel. max Rel. min increasing decreasing increasing

  17. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. 4. Identify any inflection point(s) and also find concave up/down. 5. Sketch the graph Rel. max Rel. min Rel. max Rel. min Absolute max Absolute min This is the smallest relative min value… This is the largest relative max value… increasing decreasing increasing

  18. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. 4. Identify any inflection point(s) and also find concave up/down. 5. Sketch the graph ( inflection point ) CD CU CU CD Rel. max Rel. min Rel. max Rel. min Absolute max Absolute min

  19. Sketching Functions 1. Get your critical point(s) and find increasing decreasing. 2. Identify all relative max and min. 3. Identify any absolute max and min. 4. Identify any inflection point(s) and also find concave up/down. 5. Sketch the graph ( inflection point ) CD CU CU CD Rel. max Rel. min Rel. max Rel. min 5 Absolute max Absolute min 5

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