Derivatives
See how a secant line becomes a tangent as the second point moves closer.
Gradient of secant line = [f(x+h) - f(x)] / h
Average rate of change over an interval that you can change by adjusting h.
Function graph
Purple = point at x, pink = point at x+h
Curve: x²
Tangent: purple
Secant: dotted pink
Values
x = 1.000
h = 0.500
x+h = 1.500
f(x) = 1.000
f(x+h) = 2.250
secant gradient = 2.500
tangent gradient = 2.000
h = 0.500
x+h = 1.500
f(x) = 1.000
f(x+h) = 2.250
secant gradient = 2.500
tangent gradient = 2.000
[2.250 - 1.000] / 0.500 = 2.500
Function
f(x) = x²
Point controls
Concept
The secant slope measures the average rate of change from x to x+h.
As h gets closer to 0, the secant approaches the tangent.
This page is basic currently but I'm stuck on what else to add. Possibly a little guide on differentiation from first principles.