Mathematical Methods · differential calculus · manipulative

From secant to tangent — first principles

Shrink h and watch the secant through x and x + h fall onto the tangent. The difference quotient approaches f′(x).

y = f(x) secant limiting tangent (opt.)

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Point x

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h = 0 is undefined — use a tiny |h| to see the limit.

Show limiting tangent
optional — the secant already shows the job

Difference quotient

[f(x+h) − f(x)] / h
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Working