# Search Results for “functions”

By Duncan
##### Find the Multiple 4
Another mystery curve.  Can you find what multiple of sin(x) it is?

Tags: functions

##### 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

##### Basic Derivatives
Drag the point to see how the slope of the line relates to the x value of the point at which it’s tangent to the function. Can you figure out what the function is, based on the values of the x and y coordinates? The slope of the line can also be represented in terms of x; can you figure out what this representation is? This representation is the derivative of the entire function, not just at a single point. This is called the derivative of the function, and can be notated by, for example, the derivative of F(x) = F’(x), although there are many other notations as well.

Tags: Calculus, Derivatives, Functions

By Duncan
##### Function Product Challenge 3
This time h(x) is unknown.  Can you find f(x) so that f(x)*sin(x) = h(x)?

Tags: functions

By Duncan
##### function product challenge 2
Can you find f(x) such that f(x)*g(x) = h(x)  (Yes, you could use f(x) = h(x)/g(x), but be more elegant!!)

Tags: functions

By Duncan
##### Function Product Challenge 1
Can you define f(x) so that the red curve lies on top of the grey one?

Tags: functions, function-products, trigonometry

##### Exploration of The Mean Value Theorem
Try different functions to explore The Mean Value Theorem.

Tags: calculus

##### Rotating Ellipses
Two ellipses rotate within a third such that the two smaller ellipses are always tangent to each other and the larger ellipse. Adjusting the variable X demonstrates this rotation. All three ellipses are constrained only by their implicit equations, and the moving ellipses' equations include functions of X that allow them to rotate. Can you figure out what the equations are (the other constants in the equations are a, b, h, and k)?

Tags: Ellipses, conics, puzzler