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Tangent and normal lines
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Learn it The slope of the tangent at x = a is f′(a). Its equation: y − f(a) = f′(a)(x − a). The normal is perpendicular to the tangent, with slope −1/f′(a).
Example: Tangent to y = x² − 3x at x = 4.
- f(4) = 4, f′(x) = 2x − 3 → f′(4) = 5.
- y − 4 = 5(x − 4) → y = 5x − 16.
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