How to find the slope of any curve
👆 Drag the point along the curve
How do you find the slope of a curved line? Unlike straight lines, curves change direction constantly. The slope is different at every point!
At any point on a curve, we can draw a line that just "touches" it — the tangent line. The slope of this tangent tells us how steep the curve is at that exact point.
The derivative f'(x) is a formula that gives you the slope of the tangent at any point x. For x², the derivative is 2x. So at x=3, the slope is 2×3 = 6!
The derivative comes from taking two points very close together on the curve, drawing a line through them, and seeing what happens as they get infinitely close. That line becomes the tangent!