3.6 – Critical Points & Extrema
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Transcript of 3.6 – Critical Points & Extrema
3.6 – Critical Points & Extrema
Vocabulary• Critical Points – points on a graph in which
a line drawn tangent to the curve is horizontal or vertical– Maximum– Minimum– Point of Inflection
Maximum
• When the graph of a function is increasing to the left of x = c and decreasing to the right of x = c.
Minimum
• When the graph of a function is decreasing to the left of x = c and increasing to the right of x = c
Relative Extrema
• A maximum/minimum of a function in a specific interval.
• It is not necessarily the max/min for the entire function
Absolute Extrema• Extrema – the general term of a maximum
or minimum.
• Absolute Extrema – the greatest/smallest value of a function over its whole domain
Point of Inflection
• Not a maximum or minimum
• “Leveling-off Point”
• When a tangent line is drawn here, it is vertical
Testing for Critical Pointslet x = a be the critical point for f(x)h is a small value greater than zero
Maximum
f(a – h) < f(a)
f(a + h) < f(a)
Minimum
f(a – h) > f(a)
f(a + h) > f(a)
Point of Inflection
f(a – h) > f(a)
f(a + h) < f(a)
Point of Inflection
f(a – h) < f(a)
f(a + h) > f(a)
Pictures will be drawn on the board
Let’s Look at Page 176
# 4 – 5, 8 – 11
We will do these together as examples