# 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?##### 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?