The Curved Line Slope Calculator finds the slope of a curve at a selected point. For a straight line, one slope describes the entire line, but a curve can have a different slope at every point.
Slope of a Curve
If y=f(x), the instantaneous slope at x is fβ²(x). Geometrically, this is the slope of the tangent line touching the curve at that point. A positive derivative means the curve rises locally, while a negative derivative means it falls.
How to Use the Calculator
Enter the function and the x-value requested by the tool. The point must be associated with the function, so if the calculator asks for both coordinates, make sure they agree with the equation.
Example
For y=xΒ³, the derivative is 3xΒ². At x=2, the slope is 12. This means the tangent line at that location rises much more sharply than it does near x=0.
Connection With Tangent Lines
Once the slope and point are known, the tangent line can be written as yβyβ=m(xβxβ). The slope calculator therefore provides the key quantity needed to construct the local linear approximation.
Why Point Selection Matters
Two nearby points on a curve can have noticeably different slopes. A secant slope between two points is an average rate of change, while the derivative at one point is the instantaneous rate. Do not confuse these two measurements.