## How do you use the racetrack principle?

This principle is derived from the fact that if a horse named Frank Fleetfeet always runs faster than a horse named Greg Gooseleg, then if Frank and Greg start a race from the same place and the same time, then Frank will win. More briefly, the horse that starts fast and stays fast wins.

**What is the racetrack principle calculus?**

The racetrack principle argues that if two objects begin at the same place and the same time and one is traveling faster than the other, then the faster object will be ahead of the slower object.

### What is the increasing function theorem?

The Increasing Function Theorem Suppose that f is continuous on a ≤ x ≤ b and differentiable on aIf f/(x) > 0 on a. If f/(x) ≥ 0 on a

**What is Rolle’s and Lagrange’s theorem?**

Algebraically, this theorem tells us that if f (x) is representing a polynomial function in x and the two roots of the equation f(x) = 0 are x =a and x = b, then there exists at least one root of the equation f'(x) = 0 lying between these values.

#### What does F X greater than 0 mean?

The solution set of the inequality ‘f(x)≥0 f ( x ) ≥ 0 ‘ is shown in purple. It is the set of all values of x for which f(x) is nonnegative. That is, it is the set of x -values that correspond to. the part of the graph that is either on or above the x -axis.

**What is a decreasing function?**

: a function whose value decreases as the independent variable increases over a given range.

## Is an endpoint a critical point?

Critical Points A critical point is an interior point in the domain of a function at which f ‘ (x) = 0 or f ‘ does not exist. So the only possible candidates for the x-coordinate of an extreme point are the critical points and the endpoints.

**What is Rolle’s theorem with example?**

rolle’s theorem examples (b) f(x)=x3−x f ( x ) = x 3 − x being a polynomial function is everywhere continuous and differentiable. Also, f(−1)=f(1)=0. f ( − 1 ) = f ( 1 ) = 0.