# Search Results for “Calculus”

##### Sliding Ladder Problem

One of the first calculus class problems is the sliding ladder. In this problem, a ladder is resting against a wall when, all of a sudden, it starts sliding down! In this problem you're solving for dx/dt or the rate at which the point B is moving away from the wall (point C). Input constraints: -The rate of slide must be negative for the ladder to slide down -The initial height of the ladder must be less than the ladders length##### 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

If f(2) = -2 and f'(x) >=2 for 2<=x<=6, how small can f(6) possibly be?##### 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?##### 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?##### 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.