# Search Results for “point”

##### Exploring Rolle's Theorem

Explore conditions of the Rolle's Theorem. The applet shows the graph of continuous differentiable function f(x) on a closed interval [a, b].**Case 1**. f(x) < f(a) for some x inside the interval (a, b). Can you find the number c such that f'(c)=0? What did you notice about the point when f'(c)=0?

**Case 2.**f(x) > f(a) for some x inside the interval (a, b). Can you find the number c such that f'(c)=0? What did you notice about the point when f'(c)=0? Can a given function have more than one number on a given interval such that f'(c)=0?

##### Epic Circle Trace

A line passes intersects a circle at two points. Each point is located proportionally around the circle in terms of a given function of**t**. The path of the line’s movement is traced as

**t**varies. Try changing/animating

**t**. Can you figure out how each point is constrained, in terms of

**t**? Look at the gx source file for the answer.

*Hint: look at the period of the movement, and how it changes as*

**t**changes.