# How do you describe a parametric curve?

## How do you describe a parametric curve?

Each value of t defines a point (x,y)=(f(t),g(t)) ( x , y ) = ( f ( t ) , g ( t ) ) that we can plot. The collection of points that we get by letting t be all possible values is the graph of the parametric equations and is called the parametric curve.

## How do you find the concavity of a parametric curve?

The concavity of a parametric curve at a point can be determined by computing d2y/dx2 = d(dy/dx)/dt/(dx/dt), where dy/dt is best represented as a function of t, not x. The curve is concave up when d2y/dx2 is positive, and concave down if it is negative.

**How do you find concavity?**

We can calculate the second derivative to determine the concavity of the function’s curve at any point.

- Calculate the second derivative.
- Substitute the value of x.
- If f “(x) > 0, the graph is concave upward at that value of x.
- If f “(x) = 0, the graph may have a point of inflection at that value of x.

### How do you determine if a curve is concave up or down?

If f “(x) > 0, the graph is concave upward at that value of x. If f “(x) = 0, the graph may have a point of inflection at that value of x. To check, consider the value of f “(x) at values of x to either side of the point of interest. If f “(x) < 0, the graph is concave downward at that value of x.

### How do you tell if graph is concave up or down?

In order to find what concavity it is changing from and to, you plug in numbers on either side of the inflection point. if the result is negative, the graph is concave down and if it is positive the graph is concave up.

**What is orientation of parametric curve?**

The direction of the plane curve as the parameter increases is called the orientation of the curve. The orientation of a plane curve can be represented by arrows drawn along the curve. Examine the graph below. It is defined by the parametric equations x = cos(t), y = sin(t), 0≤t < 2Π.

## What are parametric curves used for?

Parametric equations can be used to describe all types of curves that can be represented on a plane but are most often used in situations where curves on a Cartesian plane cannot be described by functions (e.g., when a curve crosses itself).

## For which values of T is the parametric curve concave upward?

so the curve is concave up. If t > 0, the denominator is positive, but the numerator is positive when t > 1. Thus the curve is concave up for t < 0 and t > 1.

**How do you know when a function is concave up or down?**

Taking the second derivative actually tells us if the slope continually increases or decreases.

- When the second derivative is positive, the function is concave upward.
- When the second derivative is negative, the function is concave downward.

### How do you know if a curve is concave or convex?

To find out if it is concave or convex, look at the second derivative. If the result is positive, it is convex. If it is negative, then it is concave.

### What marks the change in the curve concavity?

Of particular interest are points at which the concavity changes from up to down or down to up; such points are called inflection points.

**How do you determine the open intervals on which the graph is concave upward or concave downward?**

The second derivative of a function may also be used to determine the general shape of its graph on selected intervals. A function is said to be concave upward on an interval if f″(x) > 0 at each point in the interval and concave downward on an interval if f″(x) < 0 at each point in the interval.

## How do you test for concavity?

To find when a function is concave, you must first take the 2nd derivative, then set it equal to 0, and then find between which zero values the function is negative. Now test values on all sides of these to find when the function is negative, and therefore decreasing.