210 m4p1 secant to tangent
Instructions
Click on the red point, (b,f(b)). Drag that red point to see how the secant line to f changes.
Notice that as the red point moves towards the blue point, (a,f(a)), the secant line to f overlaps the green dotted line (the tangent line to f). They become the same line!
Key concept: As x=b gets moved closer and closer to x=a, the secant line approaches the tangent line. So, the average rate of change (slope of the secant line) approaches the instantaneous rate of change (the slope of the tangent line) which is how the derivative is defined. (Derivative = slope of tangent line = instantaneous rate of change.)