There isn't any "true" answer for tangent line. As you said, it all depends at which point on the curve you choose to evaluate the tangent line. Think about it this way: Suppose y=x+3. What is the "true" value of y here?aznHypnotix said:A tangent to a curve is a line that touches the curve but at what specific point where there is a slope to the curve. Equations like y = X^2 have many slopes because the curve is shaped differently at different points. We can choose 2 points on the graph and find the slope but it will different all the time. What is a true answer for tangent line?
A tangent line is a straight line that touches a curve at only one point. It represents the instantaneous slope of the curve at that point.
To find the slope of a tangent line, you can use the derivative of the function at the point of interest. This will give you the slope of the curve at that specific point.
The equation for a tangent line can be written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.
No, a curve can only have one tangent line at a given point. This is because a tangent line represents the instantaneous slope of the curve at that point, and there can only be one instantaneous slope.
Finding tangent lines can be useful in many real-life situations, such as in engineering, physics, and economics. It can help us understand the rate of change of a variable at a specific point, which is important in predicting and analyzing various systems and processes.