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)Point of Inflection: a point where the graph changes its curvature.

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

To find a point in the calculator

1) Use your best estimate to locate a point2) 2nd – calc- max/min3) Place curser on left, enter. Place curser on right, enter. Enter

Graph the following examples and pick out the critical pointsF(x) = 5x3 -10x2 – 20x + 7

F(x) = 2x5 -5x4 –10x3.