- #1
bonzy87
- 5
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Verify that (1,1) is a point on the graph of y + ln xy = 1 and find the equation of the tangent line at (1,1) to this graph
how do you go about answering this?
how do you go about answering this?
A plot of points is a graphical representation of a set of data points on a coordinate plane. Each point is represented by an ordered pair (x, y) where x is the horizontal value and y is the vertical value.
To plot points, you need to have a set of data points with their corresponding x and y values. Then, you can plot each point on a coordinate plane by marking the x and y values on the horizontal and vertical axes, respectively. The points can be connected to form a line or curve, depending on the type of data being represented.
A tangent line is a straight line that touches a curve or function at only one point, known as the point of tangency. It represents the instantaneous rate of change of the curve at that point.
The equation of a tangent line can be found using the point-slope form of a line: y - y1 = m(x - x1), where m is the slope of the tangent line and (x1, y1) is the point of tangency. To find the slope, you can take the derivative of the function at the point of tangency and substitute the x-value into the derivative. Finally, plug in the slope and the point of tangency into the point-slope form to get the equation of the tangent line.
Finding the equation of a tangent line is important because it helps us understand the behavior of a curve or function at a specific point. It also allows us to approximate the value of the function at that point and make predictions about its future behavior. Additionally, the slope of the tangent line can provide insight into the rate of change of the function at that point, which is useful in many real-world applications.