1. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Section 7.5 Antiderivatives - Graphical/Numerical

2. What does the graph of the derivative tell us about the function? Recall: Section 2.2

3. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Antiderivatives The function F(x) is an antiderivative of f(x) if F ′(x) = f(x). Example: if F’(x)=3, find 17 different antiderivatives, F(x). But, if I tell you that F(0)=3….?

4. Exercise 1

5. Exercise 2 Complete the table. 01234567 7 0 2 5 5 6.5 5 3 2

6. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Matching a function with its antiderivative Which of the following graphs (a)-(d) could represent an antiderivative of the function shown in Figure 7.2?

7. Matching a function with its antiderivative Which of the following graphs (a)-(d) could represent an antiderivative of the function shown in Figure 7.3?

8. What does the graph of the derivative tell us about the function? The figure below shows a graph of y = f(x) with some areas labeled. Assume F ʹ (x) = f (x) and F(0) = 10. Then F(5) = F(5) = 10 + 7 – 6 = 11

9. What does the graph of the derivative tell us about the function? The figure below shows a graph of y = F ʹ (x). Where does F(x) have a local maximum? A local minimum? F has local maxima at 2 and 8. F has local minima at 0 and 6.