Section 2.5 Concavity. Lines are functions with constant rates of change What if we have increasing or decreasing rates of change? –What happens with.

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Presentation transcript:

Section 2.5 Concavity

Lines are functions with constant rates of change What if we have increasing or decreasing rates of change? –What happens with our graph if our rate of change is increasing? –What happens if it is decreasing?

t, time (hours) D, Mike’s distance (miles) Average speed, Δd/ Δt (mph) t, time (hours) D, Jen’s distance (miles) Average speed, Δd/ Δt (mph) Describe the difference in the two data sets How do they differ? You may want to use rates of change to help

t, time (hours) D, Mike’s distance (miles) Average speed, Δd/ Δt (mph) (mph) 19 (mph) 23 (mph) 27 (mph) t, time (hours) D, Jen’s distance (miles) Average speed, Δd/ Δt (mph) (mph) 22 (mph) 20 (mph) 19 (mph) Graph the distance of each cyclist Describe the shape of the graph and explain the shape using average rate of change

When the graph bends upward (as in Mike’s case) we say the graph is concave up –Thus when the rate of change is increasing, our function is concave up When the graph bends downward (as in Jen’s case) we say the graph is concave down –Thus when the rate of change is decreasing, our function is concave down Is there any relationship between whether a graph is increasing/decreasing and concave up/down?

Concave up and increasing!!!

Concave up and decreasing!!!

Concave down and increasing!!!

Concave down and decreasing!!!

In your groups try problems 1, 15, and 19