derivative and tangent
To show that the derivative is the slope of tangent
The function, , is shown in dark green. The derivative, , is in light green.
Two points, A and B are along the curve. These points, A and B, can be moved along the curve.
A tangent line at point A is shown in red.
A line AB is shown running through the two points A and B. This line is in blue.
As B is move towards or away from A, the slope of line AB changes. As B gets closer to A, this slope gets closer to the slope of the tangent at A.
The value of the derivative is shown for the same value of x as point A. This is the same value as the slope of the tangent.