Search Results for “Function”
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!!)
Function Product Challenge 3
This time h(x) is unknown. Can you find f(x) so that f(x)*sin(x) = h(x)?
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.
Application of The Mean Value Theorem to problem solving
Given function f(x) = arctan (1-x) on the interval [0, 1].
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 Rolle's Theorem
Apply Rolle's Theorem to solve problems. Given function C(x) = 6(1/x + x/(x+4)).
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.
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?
