In our day to day life, a curve is defined as a line which is not straight. But, in math, a curve can also be straight or it is also called continuous line. Curve has certain properties. In this topic you could see types of curve and region of a curve, which is mentioned below.
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Based on these properties, curves are classified into two types.
Open curve is defined as a curve whose ends do not meet. Example is parabola, hyperbola.
Closed curves are curves whose ends are joined. Closed curves do not have end points. Examples of closed curves are ellipse and circle.
When we discuss about a curve, let us see points L, M and N on the curve given below.
N is outside the curve, so it is present in the exterior of the curve.
M is on the boundary of the curve, while L lies inside the curve that is interior of the curve.
The boundary along with the interior portion of a curve is called as the region of a curve. Two dimensional curves are algebraically represented as polynomials in variable x and y. We can plot the curve on a graph paper. The curve is symmetrical about:
When we sketch a curve, we have to see for x intercept, y intercept, local minima, local maxima, and points of inflection are taken into consideration. There are some steps to be followed to find all these.
If `(d^(2)y)/dx^2` > 0, the curve is concave up.
If `(d^(2)y)/dx^2` < 0, the curve is concave down.
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