Final answer:
To find the slope of the tangent line at a given point, calculate the derivative of the function and substitute the x-coordinate of the point into the derivative. This value is the slope of the tangent line at that point.
Step-by-step explanation:
To find the slope of the tangent line at a given point on a curve, you would use calculus, specifically the concept of derivatives. The slope at any point on a curve is given by the derivative of the function at that point. Here is the step-by-step process:
- Step 1: Identify the function f(x) that defines the curve.
- Step 2: Compute the derivative of the function, f'(x), to find the general formula for the slope of the tangent line at any point x.
- Step 3: Substitute the x-coordinate of the given point into the derivative to calculate the specific slope of the tangent line at that point.
- Step 4: The resulting number is the slope of the tangent line at the given point.
For example, if your function is f(x) = x^2, and you want to find the slope of the tangent line at x = 3, you would first find the derivative, f'(x) = 2x, and then substitute x = 3 to get the slope, which is f'(3) = 6.