A tangent line to a function is a line that touches the function at exactly one point. This point of tangency has the same slope as the function at that point.
To find the equation of a tangent line to a function, you need to first find the derivative of the function. Then, you can use the point-slope form of a line to plug in the coordinates of the point of tangency and the slope of the function at that point.
In calculus, the tangent line is used to approximate the behavior of a function at a specific point. It can also help us find the instantaneous rate of change, or the derivative, of a function.
No, a function can only have one tangent line at a point. This is because a tangent line must touch the function at exactly one point and have the same slope as the function at that point.
The slope of a tangent line is equal to the derivative of the function at the point of tangency. This means that the derivative gives us the slope of the tangent line, and vice versa.