The Curved Line Slope Calculator finds the slope of a curve at a selected point by using the derivative. Unlike the slope between two points on a straight line, this is a local rate of change.
Formula for the slope of a curve
For a differentiable function y = f(x), the slope at x = a is f'(a). The derivative gives the slope of the tangent line touching the curve at that point.
Worked example
Take f(x) = xΒ² + 2x. Its derivative is f'(x) = 2x + 2. At x = 3, the slope is 2(3) + 2 = 8. So the curve is rising with a local slope of 8 at x = 3.
Using the calculator
- Enter the function.
- Enter the x-value where the slope is required.
- Differentiate the function.
- Evaluate the derivative at that x-value.
A positive result means the curve is increasing at the chosen point; a negative result means it is decreasing.