To find the slope of a curve at a specific point, we need to determine the derivative of the function that describes the curve. The derivative gives us the slope of the tangent line to the curve at any given point.
Follow these steps:
- Identify the function: Let’s denote the function as f(x).
- Differentiate the function: Calculate f'(x), the derivative of f with respect to x. This can be done using basic differentiation rules.
- Evaluate the derivative at the given point: Substitute the x-coordinate of the indicated point into the derivative f'(x) to find the slope at that specific point.
For example, if we have a function f(x) = x² and we want to find the slope at the point (2, f(2)), we first find the derivative f'(x) = 2x. Then, substituting x = 2 gives us f'(2) = 2(2) = 4. Thus, the slope of the curve at the point (2,4) is 4.
Using this method will allow you to find the slope of any curve at any point you are interested in.