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3.6 Critical Points and Extrema. Objective: Find the extrema of a function. Critical Points:. Points at which the nature of a graph changes. (points at which a line drawn tangent to the curve is horizontal or vertical). 3 Types of Critical Points:. -Maximums -Minimums -Points of Inflection.
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3.6 Critical Points and Extrema Objective: Find the extrema of a function.
Critical Points: Points at which the nature of a graph changes. (points at which a line drawn tangent to the curve is horizontal or vertical) 3 Types of Critical Points: -Maximums -Minimums -Points of Inflection Absolute Max: A point that represents the maximum value a function assumes over its domain.
Absolute Min.: A point that represents the minimum value a function assumes over its domain. A max. or min. value of a function. A point that represents the max. or min. for a certain interval. Extremum: Relative Extrema:
Ex. 1) Locate the extrema for the graph of y=f(x). Name and classify the extrema of the function. Ex. 2) Use a graphing calculator to graph f(x) = x³ - 8x + 3 and to determine and classify its extrema. See pg. 174 table.
Ex. 3) The function f(x) = 3x^4 – 4x³ has critical points at x=0 and x=1. Determine whether each of these critical points is the location of a max., min., or a point of inflection. Ex. 4) One hour after x milligrams of particular drug are given to person, the rise in body temp., T(x), in degrees Fahrenheit is given by T(x)= x – (x²/9). The model has a critical point at x= 4.5. a.)Determine if this critical point is a max. b.) Why should a doctor be aware of this critical point?
