This activity is built for students to explore the Fundemental Theorem of Calculus. Notice the questions that go along with the file at the bottom of the page.

The checkboxes on the right allow you to click through the assignment. Check each box referenced and then answer the questions that accompany it.
Fundemental Theorem of Calculus

Read through the formula, try to have it make sense to you before moving forward. If you need to make notes or verify any of it on a piece of paper do it!

f(x)

Display the function; Notice the color coding from the theorem above and the sliders that control the values. Adjust the values on the sliders to pick a function that has at least one local extreme value in the graphing window.

F(x)

Display the function; Notice the color coding from the theorem above.

What does this graph represent?

Limits

Display the limits; Notice that points A and B are movable. Click and drag them in the window.

Where do these limit points appear in the formula above?

X

Display the X; Notice that the point X is movable. Click and drag it in the window.

Where does this point appear in the formula above?

What other items appear when you click-on the checkbox controlling the X point? what do these represent in the formula?

Integration

Display the Integration; Notice that the points A,B, and X are movable. Click and drag it in the window.

Explain what happens when X moves outside [A,B]. Explain why this makes sense in the formula above.

Integration

Display the Integration; Notice that the points A,B, and X are movable. Click and drag the points in the window.

Explain what happens when X moves outside [A,B]. Explain why this makes sense in the formula above.

Tangent Line

Display the Tangent Line; Notice that the points A,B, and X are movable. Click and drag it in the window.

Notice that a box with m_{tangent} appears on the screen, what does this refer to in the picture? Where is this value referenced in the formula above? What does this tell you about the slope of the tangent lines?