Final answer:
To find the equation of the tangent line to a curve at a specific point, calculate the slope of the curve at that point and use the point-slope form of a linear equation.
Step-by-step explanation:
The equation of the tangent line to a curve at a specific point can be found by calculating the slope of the curve at that point. The slope of a straight line tangent to the curve at that point is equal to the slope of the curve at that point. To find the equation of the tangent line, follow these steps:
- Find the slope of the curve at the given point.
- Determine the coordinates of the point at which the tangent line intersects the curve.
- Use the point-slope form of a linear equation, y = mx + b, where m is the slope and (x, y) are the coordinates of the intersecting point, to write the equation of the tangent line.