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## Main Question or Discussion Point

What is the difference between slope w.r.t origin and slope at a point on the curve and when are they used ?

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What is the difference between slope w.r.t origin and slope at a point on the curve and when are they used ?

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Please help with the above

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Mark44

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I just came across an example which used slope w.r.t origin. Can you please walk me through the solution

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Mark44

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I still maintain that it is not a very useful concept. The important concept is the slope of the tangent line to a curve at a point on the curve.

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No, the text does not use the terminology "slope with respect to the origin", now that I've come across this example I thought that there might exist such a concept.

I still maintain that it is not a very useful concept. The important concept is the slope of the tangent line to a curve at a point on the curve.

Don't you think the smallest slope is at point where the first line segment meets the curve in the Fig. 4.26 ? (If we consider the slope at a point on the curve).

Here's the question for the previous solution.

BTW, the Fig. 4.25 is same as the Fig.4.26

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Mark44

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No, but that's a reasonable question. You have to distinguish between "slope at a point on the curve" and "slope of the segment to a point on the curve." In the solution for Example 5, it says, "Figure 4.26 shows that g/v is the slope of the line from the origin to the point P."No, the text does not use the terminology "slope with respect to the origin", now that I've come across this example I thought that there might exist such a concept.

Don't you think the smallest slope is at point where the first line segment meets the curve in the Fig. 4.26 ? (If we consider the slope at a point on the curve).

In the image of Fig. 4.26, the slope of the tangent line at the left-most point is less than at the other two points shown in this graph, but that's not what they're comparing.

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