Search Results for “Polar-function”

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?

Tags: calculus

Application of Rolle's Theorem
Apply Rolle's Theorem to solve problems. Given function C(x) = 6(1/x + x/(x+4)).

Tags: calculus

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?

Tags: Calclulus

Area Under Sine (draggable)
Observe the definite integral of sine, or the area between the function sin(x) and the x axis, and how it changes between different bounds by dragging the boundaries, a and b. What happens to the area when the interval is 2Π? Why?

Tags: Calculus, Defininte-Integral, Sine, Draggable

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.

Tags: Trace, puzzler, circle, proportional-points, functions