Search Results for “function-draggable-curve”
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.
Application of Rolle's Theorem
Apply Rolle's Theorem to solve problems. Given function C(x) = 6(1/x + x/(x+4)).
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?
Application of The Mean Value Theorem to problem solving
Given function f(x) = (x+1)/(x-1). Show that there is no such c that f(3) = f'(c)(3-0). Why does this not contradict the Mean Value Theorem?
Application of The Mean Value Theorem to problem solving
Given function f(x) = arctan (1-x) on the interval [0, 1].
Rolling Parabola
If you roll a parabola along the ground, what curve does its focus trace out? It might look like a parabola, but is it?
Maximum Area Triangle
The app uses a physical model to find the largest area triangle whose vertices lie on a smooth closed curve (defined by the red control points). The triangle defined by the tangent lines at the vertices is displayed, along with its medians. What do you notice about the maximum?
