Matching Functions with their Derivatives

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Presentation transcript:

Matching Functions with their Derivatives Today you will look at the graphs of several functions and try to match each function with the graph of its derivative and second derivative by using the characteristics (such as relative extrema, concavity, increasing & decreasing, etc.) defined by the sign studies.

Summary Sign Study Zeros (Critical Pts) + sign study - sign study X-intercepts of graph Graph lies above x-axis Graph lies below x-axis Relative Extrema (Max + to -) (Min - to +) is increasing is decreasing Points of inflection is concave up is concave down

In the left hand column are graphs of several functions In the left hand column are graphs of several functions. In the right-hand column – in a different order – are graphs of the associated derivative functions. Match each function with its derivative. [Note: The scales on the graphs are not all the same.]

Function – Derivative Matching Activity Each of you randomly received a card with either the graph of a function, the graph of a first derivative, or the graph of the second derivative. Your task is to walk around the room and try to find the people who have the matching function, first derivative, and second derivative graphs by using the characteristics of f(x), f’(x), and f”(x) that you have discovered using the sign studies. When you think you have found your partners, check with me to see if you are correct.

Another Look at the Product Rule using a table.

Assignment A 2.10 Sect I See you tomorrow!