- #1
ACLerok
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how does tangent lines play into this problem?
http://www.eden.rutgers.edu/~cjjacob/images/calc.jpg [Broken]
http://www.eden.rutgers.edu/~cjjacob/images/calc.jpg [Broken]
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Originally posted by ACLerok
oh, i didnt realize the d's stood for the difference.
so to find F(7), I isolate y on one side of the equation and then plugin 7 for x and solve for y? what do i do for the F'(7)? slope of the line when x=7?
A tangent line is a line that touches a curve at only one point, called the point of tangency. It represents the instantaneous rate of change of the curve at that point.
To find the equation of a tangent line, you need to first find the slope of the tangent line by taking the derivative of the original function at the point of tangency. Then, you can use the point-slope formula to find the equation of the tangent line.
Tangent lines are important in calculus because they allow us to find the instantaneous rate of change of a function at a specific point. This is useful in many real-world applications, such as finding the velocity of an object at a given time or the rate of change of a chemical reaction at a specific moment.
A line is tangent to a curve if it touches the curve at only one point and has the same slope as the curve at that point. This can be determined by graphing the line and the curve and visually checking for the point of tangency.
Tangent lines have many real-life applications, such as in physics, where they can be used to find the velocity and acceleration of an object at a specific time. In economics, they can be used to analyze the marginal cost and revenue of a business. In engineering, they are used to design smooth curves for roads and bridges. Tangent lines also have applications in medicine, astronomy, and many other fields.