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STEMORIA scientific instrument
Connect changing secant slopes to the local tangent slope through synchronized mathematical views.
01
Manipulate
02
Measure
03
Interpret
Shrink a secant interval and watch its slope approach the local tangent slope. Geometry, symbolic notation, and numerical values stay linked to one mathematical state.
Visual
Mathematical model
f(x) = x²
f′(x) = 2x
secant = [f(x + Δx) − f(x)] / Δx
tangent = f′(x)
State & data
Interpretation
The secant slope measures average change across the interval from x to x + Δx. The tangent slope is the local derivative at x.
Current difference
1
As Δx becomes smaller for this smooth function, the secant slope approaches the tangent slope.