- #1
ttpp1124
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- Homework Statement
- Can someone check to see if my two points are accurate?
- Relevant Equations
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At what point(s) on the given curve is the tangent line horizontal?
- Thread starter ttpp1124
- Start date
In summary, the conversation discusses the poster's confidence in their solutions and the reassurance from online tutors. They suggest using WolframAlpha for numerical solutions and encourage the poster to have more confidence in their own abilities.
- #2
HallsofIvy
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Yes, of course it is! You have posted several questions in which you have given detailed solutions. Wonderful! My only question is why you would feel the need to ask!
- #3
ttpp1124
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It's always relieving and reassuring when I get a heads up from brilliant tutors online :)HallsofIvy said:
Thank you!
- #4
Merlin3189
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If you just want a check of a numerical solution, you could try WolframAlpha.
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- #5
HallsofIvy
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You should have more confidence in your own "brilliance".
1. What is a tangent line?
A tangent line is a line that touches a curve at only one point, without crossing through it. It represents the instantaneous rate of change of the curve at that specific point.
2. How can I find the points on a curve where the tangent line is horizontal?
To find the points where the tangent line is horizontal, you need to find the points on the curve where the slope (or rate of change) is equal to 0. This means that the curve is not changing at that point, resulting in a horizontal tangent line.
3. Why is it important to know where the tangent line is horizontal on a curve?
Knowing where the tangent line is horizontal on a curve can help us understand the behavior of the curve at that point. It can also help us determine the maximum or minimum points on the curve, as well as the concavity of the curve.
4. Can there be more than one point on a curve where the tangent line is horizontal?
Yes, there can be multiple points on a curve where the tangent line is horizontal. This can happen when the curve has a flat or constant section, or when it has a peak or valley with a horizontal tangent line at the top or bottom.
5. How do I calculate the slope of a tangent line at a specific point on a curve?
The slope of a tangent line at a specific point on a curve can be calculated using the derivative of the curve at that point. This involves finding the limit of the slope of a secant line as the two points on the curve get closer and closer together. Alternatively, you can also use the formula for the slope of a tangent line, which is the derivative of the curve at that point.
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