Section 6.1 Antiderivatives Graphically and Numerically

1. Section 6.1Antiderivatives Graphically and Numerically

2. The following is a velocity curve in ft/sec • How would we find the distance traveled between 0 and 2 seconds?

3. The following is a velocity curve in ft/sec • How would we find the distance traveled between 2 and 4 seconds?

4. The following is a velocity curve in ft/sec • How would we find the total distance traveled in the first 4 seconds?

5. The following is a velocity curve in ft/sec • Thus we can use the area under the curve to give us the change in function values

6. In the last section we began discussing area under a curve • If we had a velocity curve than the area under the curve gave us the distance traveled • We introduced the definite integral as a way of finding the net area under a curve • The net area under the curve gives us the change in the function value from a to b • We are going to use this information to see how we can recover function values give the derivative

7. Complete the worksheet • Find the area under f’ between 0 and 3 • Now use the Fundamental Theorem of Calculus to get the area under each graph you found between 0 and 3 • f and g are called antiderivatives of f’ • They have the same derivative, although they are different functions

8. Given the values of the derivative, f’(x) in the table and that f(0) = 100, estimate f(x) for x = 2, 4, 6.