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tangent line

The line that touches a curve at one point and matches its exact direction there.

The tangent line to y=f(x) at x=a is the line through \big(a, f(a)\big) whose slope is the limit of secant-line slopes as the second point slides toward a — that limiting slope is f'(a), the derivative.

Examples

  • The tangent line to y=x^2 at x=1 has slope 2 and equation y = 2x - 1.

See also

difference quotient derivative instantaneous rate of change
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