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 ),

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Presentation transcript:

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 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

Sketching Functions

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

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

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

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

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

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

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

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

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

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

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

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

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 Rel. max Rel. min

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 Rel. max Rel. min Absolute min Absolute max This is the smallest relative min value… This is the largest relative max value…

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 Absolute min Absolute max ( inflection point ) CD CU

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 Absolute min Absolute max ( inflection point ) CD CU 5 5