Graph 2-8

-Refer to Graph 2-8. In the graph shown, the slope of the curve between points A and B is:

Question

Graph 2-8
 
-Refer to Graph 2-8. In the graph shown, the slope of the curve between points A and B is:

Quizplus · Accepted Answer

The slope of a curve at any point is given by the derivative of that curve at that point. The derivative of a function f(x) is given by f'(x). Looking at the curve between points A and B, we can see that the curve is a straight line, which means that the slope is constant between these two points. To find the slope, we can take any two points on this line and use the slope formula:

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

Let's take points A and B:

slope = (2 - 3) / (1 - 0) = -1

Therefore, the slope of the line between points A and B is -1. But we need to choose the slope of the curve, not the line. Since we know that the slope is constant for this line, we can say that the slope of the curve is also -1. However, we need to express the slope as a fraction, so we divide by the horizontal distance between the two points (which is 2 - 0 = 2):

slope = -1 / 2 = -1/2

Therefore, the best choice is B) -1/2.

Graph 2-8 -Refer to Graph 2-8. in the Graph Shown, the Slope