What do you need for curve sketching?
What do you need for curve sketching?
The following steps are taken in the process of curve sketching:
- Domain. Find the domain of the function and determine the points of discontinuity (if any).
- Intercepts.
- Symmetry.
- Asymptotes.
- Intervals of Increase and Decrease.
- Local Maximum and Minimum.
- Concavity/Convexity and Points of Inflection.
- Graph of the Function.
WHAT IS curve sketching used for?
In geometry, curve sketching (or curve tracing) are techniques for producing a rough idea of overall shape of a plane curve given its equation, without computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features.
How many turning points are there?
Higher degree
| Type of polynomial | Number of x-intercepts | Number of turning points |
|---|---|---|
| linear | 1 | 0 |
| quadratic | from 0 to 2 | 1 |
| cubic | from 1 to 3 | 0 or 2 |
| quartic | from 0 to 4 | 1 or 3 |
How do you find transition points?
Transistion and inflection point The transition is between concavities (upward or downward). The points c = 0 and c = 1/4 are included in the domain of the function f; their second derivative are zero, then they are the transition numbers of the function f.
How do you read a curved graph?
An upward-sloping curve suggests a positive relationship between two variables. A downward-sloping curve suggests a negative relationship between two variables. The slope of a curve is the ratio of the vertical change to the horizontal change between two points on the curve.
How do you tell if a critical point is a max or min?
Determine whether each of these critical points is the location of a maximum, minimum, or point of inflection. For each value, test an x-value slightly smaller and slightly larger than that x-value. If both are smaller than f(x), then it is a maximum. If both are larger than f(x), then it is a minimum.
