Function:
Secant Line Approaching Tangent as h ➔ 0
Secant LineTangent Line
Position of P (a):1
Offset h (Q approaches P):1.5
Limiting Slope Calculations
Difference Quotient (Secant Slope):
Δy/h = 3.5
[f(a+h) − f(a)] / hTrue Derivative f′(a) (Tangent Slope):
2
lim (h ➔ 0) of difference quotientDerivative Sign Behavior
📈 f′(x) > 0: Function is strictly INCREASING at this point.
As the secant interval $h$ shrinks toward zero, the secant line between two separate points coalesces into the instantaneous tangent line at point P.
🔗Connected Mathematical Concepts
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