To find the equation of a tangent line to a curve, you need to first find the slope of the curve at the point where the tangent line intersects it. This can be done by taking the derivative of the curve at that point. Then, using the point-slope formula, you can plug in the slope and the coordinates of the point to find the equation of the tangent line.
The point-slope formula is y - y1 = m(x - x1), where m is the slope of the tangent line and (x1, y1) is the point where the tangent line intersects the curve.
Yes, you can find the equation of a tangent line to a curve at any point as long as the curve is differentiable at that point. This means that the curve must have a well-defined slope at that point.
A curve is differentiable at a certain point if the limit of the slope of the curve at that point exists. In other words, the slope of the curve must approach a well-defined value as the distance between the point and the chosen point on the curve becomes smaller and smaller.
Yes, there are other methods for finding the equation of a tangent line to a curve, such as using the slope-intercept form of a line or the two-point form of a line. However, the most commonly used method is the point-slope formula, as it involves finding the slope of the curve at a specific point.