Mathematics Exam > Mathematics Videos > Calculus > Tangent Lines and Rates of Change- 2
Tangent Lines and Rates of Change- 2 Video Lecture | Calculus - Mathematics
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FAQs on Tangent Lines and Rates of Change- 2 Video Lecture - Calculus - Mathematics
| 1. What is a tangent line? |  |
Ans. A tangent line is a line that touches a curve at a single point and has the same slope as the curve at that point. It represents the instantaneous rate of change of the curve at that particular point.
| 2. How do you find the equation of a tangent line? | |
Ans. To find the equation of a tangent line to a curve at a given point, follow these steps:
1. Find the derivative of the curve to determine its slope at the given point.
2. Plug the x-coordinate of the given point into the derivative to find the slope.
3. Use the point-slope form of a line (y - y1 = m(x - x1)) and substitute the values of the given point and the slope.
| 3. What is the relationship between tangent lines and rates of change? | |
Ans. Tangent lines represent the rates of change of a curve at a specific point. The slope of the tangent line is equal to the instantaneous rate of change of the curve at that point. By finding the equation of the tangent line, we can determine the rate at which the curve is changing at that particular point.
| 4. How can tangent lines be used to approximate values? | |
Ans. Tangent lines can be used to approximate values by employing linearization. By finding the equation of the tangent line at a specific point, we can use this linear approximation to estimate the value of the function near that point. This technique is especially useful when dealing with complex or non-linear functions.
| 5. Can tangent lines have multiple points of contact with a curve? | |
Ans. No, tangent lines can only have a single point of contact with a curve. The tangent line represents the slope of the curve at that specific point, and any additional points of contact would imply different slopes. If a line has multiple points of contact with a curve, it is referred to as a secant line rather than a tangent line.
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Dec 23, 2024 Last updated |
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