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3.6 Critical Points

3.6 Critical Points. Critical Points. . Maximum : When the graph is increasing to the left of x = c and decreasing to the right of x = c (top of hill) Minimum : When the graph of a function is decreasing to the left of x = c and increasing ot the right of x = c (bottom of valley)

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3.6 Critical Points

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  1. 3.6 Critical Points

  2. Critical Points .Maximum: When the graph is increasing to the left of x = c and decreasing to the right of x = c (top of hill) Minimum: When the graph of a function is decreasing to the left of x = c and increasing ot the right of x = c (bottom of valley) Point of Inflection: a point where the graph changes its curvature.

  3. Extremum – a minimum or maximum value of a function • Relative Extremum– a point that represents the maximum or minimum for a certain interval • Absolute Maximum – the greatest value that a function assumes over its domain • Relative Maximum – a point that represents the maximum for a certain interval (highest point compared to neighbors ) • Absolute Minimum – the least value that a function assumes over its domain • Relative Minimum – a point that represents the minimum for a certain interval (minimum compared to neighbourhors0

  4. To find a point in the calculator • Use your best estimate to locate a point • 2nd – calc- max/min • Place curser on left, enter. Place curser on right, enter. Enter

  5. Graph the following examples and pick out the critical points • F(x) = 5x3 -10x2 – 20x + 7 • F(x) = 2x5 -5x4 –10x3.

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