Is Slope Purely a Geometric Concept and is it Defined for a Single Point?
Is “slope” purely a geometric concept? For instance can we talk about the “slope” of a function or only the “slope” of a straight line? Furthermore, can we define “slope” for a single point? We often say the slope of the curve at a point, but how can a single point have a slope?
calculus derivatives
asked Nov 26 at 21:41
J. Smith
241
add a comment |
Is “slope” purely a geometric concept? For instance can we talk about the “slope” of a function or only the “slope” of a straight line? Furthermore, can we define “slope” for a single point? We often say the slope of the curve at a point, but how can a single point have a slope?
calculus derivatives
asked Nov 26 at 21:41
J. Smith
241
The point doesn't have a slope, and nobody says it does. The curve has a slope at a point. Consider: Noon on Wednesday is a particular time. We don't normally think of it as having a sound. But Puddles the puppy might have a sound at noon on Wednesday.
– MJD
Nov 26 at 22:13
add a comment |
Is “slope” purely a geometric concept? For instance can we talk about the “slope” of a function or only the “slope” of a straight line? Furthermore, can we define “slope” for a single point? We often say the slope of the curve at a point, but how can a single point have a slope?
calculus derivatives
asked Nov 26 at 21:41
J. Smith
241
Is “slope” purely a geometric concept? For instance can we talk about the “slope” of a function or only the “slope” of a straight line? Furthermore, can we define “slope” for a single point? We often say the slope of the curve at a point, but how can a single point have a slope?
calculus derivatives
calculus derivatives
asked Nov 26 at 21:41
J. Smith
241
asked Nov 26 at 21:41
J. Smith
241
asked Nov 26 at 21:41
J. Smith
241
asked Nov 26 at 21:41
J. Smith
241
asked Nov 26 at 21:41
J. Smith
241
241
The point doesn't have a slope, and nobody says it does. The curve has a slope at a point. Consider: Noon on Wednesday is a particular time. We don't normally think of it as having a sound. But Puddles the puppy might have a sound at noon on Wednesday.
– MJD
Nov 26 at 22:13
add a comment |
The point doesn't have a slope, and nobody says it does. The curve has a slope at a point. Consider: Noon on Wednesday is a particular time. We don't normally think of it as having a sound. But Puddles the puppy might have a sound at noon on Wednesday.
– MJD
Nov 26 at 22:13
The point doesn't have a slope, and nobody says it does. The curve has a slope at a point. Consider: Noon on Wednesday is a particular time. We don't normally think of it as having a sound. But Puddles the puppy might have a sound at noon on Wednesday.
– MJD
Nov 26 at 22:13
The point doesn't have a slope, and nobody says it does. The curve has a slope at a point. Consider: Noon on Wednesday is a particular time. We don't normally think of it as having a sound. But Puddles the puppy might have a sound at noon on Wednesday.
– MJD
Nov 26 at 22:13
add a comment |
1 Answer
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The slope is for the curve (an infinite collection of points). It just happens to vary from point to point. We can use the slope as a synonym for derivative.
answered Nov 26 at 21:45
Andrei
11k21025
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
The slope is for the curve (an infinite collection of points). It just happens to vary from point to point. We can use the slope as a synonym for derivative.
answered Nov 26 at 21:45
Andrei
11k21025
add a comment |
The slope is for the curve (an infinite collection of points). It just happens to vary from point to point. We can use the slope as a synonym for derivative.
answered Nov 26 at 21:45
Andrei
11k21025
add a comment |
The slope is for the curve (an infinite collection of points). It just happens to vary from point to point. We can use the slope as a synonym for derivative.
answered Nov 26 at 21:45
Andrei
11k21025
The slope is for the curve (an infinite collection of points). It just happens to vary from point to point. We can use the slope as a synonym for derivative.
answered Nov 26 at 21:45
Andrei
11k21025
answered Nov 26 at 21:45
Andrei
11k21025
answered Nov 26 at 21:45
Andrei
11k21025
answered Nov 26 at 21:45
Andrei
11k21025
11k21025
add a comment |
add a comment |
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The point doesn't have a slope, and nobody says it does. The curve has a slope at a point. Consider: Noon on Wednesday is a particular time. We don't normally think of it as having a sound. But Puddles the puppy might have a sound at noon on Wednesday.
– MJD
Nov 26 at 22:13