1. Section 2.5 The Second Derivative

2. The following two graphs represent the velocity a car is traveling in the first three seconds
Describe what is going on in each case v v t t

3. Complete the work sheet
What is the relationship between the concavity of the graph of f and the 2nd derivative
If f’’ > 0 over an interval, than f’ is increasing and the graph of f is concave up on that interval
If f’’ < 0 over an interval, than f’ is decreasing and the graph of f is concave down on that interval
If f’’ = 0, then we have cases
The graph of f may still be concave up or concave down
If the concavity switches, we have an inflection point

4. Is f’ positive or negative over the given periods?
The following table gives the number of passenger cars, C = f(t), in millions, in the US in the year t
Is f’ positive or negative over the given periods?
What does it tell us about the situation?
Is f’’ positive or negative over the given periods?
t (year)
1940
1950
1960
1970
1980
C (cars, in millions)
27.5
40.3
61.7
89.3
121.6