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📉 Secant to Tangent Lab

As h approaches 0,
the secant becomes the tangent

The line through two points, (a, f(a)) and (a+h, f(a+h)), on f(x)=x² is a secant line. Gradually reduce h and see what the secant slope approaches.

The derivative is defined as f'(a) = lim(h→0) [f(a+h)-f(a)] / h. In other words, the limit of the average rate of change (the secant slope) as h approaches 0 is the instantaneous rate of change (the tangent slope) at that point.

Reference point a2
Distance between the two points h1.5
Secant slope = [f(a+h) - f(a)] / h = 5.5
Current secant slope
Target tangent slope f'(a)=2a

📉 Derivative Definition Quiz

Question 1/3 · Correct 0