Question

Slope of a curve

Answer 1

One of the major difference between the slope of a straight line and that of a curve is that slope of a straight line is a constant term while the slope of a curve keeps on changing from one point to other.

In order to find out the slope of a line, we need the below-mentioned things:-

1. Identify two points on the line.
2. Select one to be (x1, y1) and the other to be (x2, y2).
3. Use the slope equation to calculate the slope.

Slope =(y2-y1)/(x2-x1)

In order to find the slope of a cure, we can use the method of a tangent. A tangent can be seen as a straight line which touches a curve at a particular point and there is no cross section of the line and the curve. The point where both the curve and line touches each other is called a point of tangency.

The slope of a curve at a point is equal to the slope of the straight line that is tangent to the curve at that point.

The slope of the curve at a point denoted as A in the figure will be equal to the straight line represented by BC. Once the slope of the straight line BC is found, this will represent the slope of a curve at that point.

The slope at point A is 1/2, or .5.

This is the slope of the curve only at point A. If we need to find out the slope of the curve in any other location or point, we can draw a straight line tangent to that point and find out the slope.

To find the slope of the curve at any other point, we would need to draw a tangent line at that