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10 cards from this deck
Line touching curve at one point with same slope as curve
Derivative gives gradient of tangent at that point
y−y1=f′(x1)(x−x1)y - y_1 = f'(x_1)(x - x_1)y−y1=f′(x1)(x−x1)
Line perpendicular to tangent at a point on curve
Product of gradients equals −1-1−1: m1m2=−1m_1 m_2 = -1m1m2=−1
−1m-\frac{1}{m}−m1 (negative reciprocal)
Point (x1,y1)(x_1, y_1)(x1,y1) on curve and derivative f′(x1)f'(x_1)f′(x1)
Function continuous and f′(x)→∞f'(x) \to \inftyf′(x)→∞ at that point
f′(x)→∞f'(x) \to \inftyf′(x)→∞ from one side, −∞-\infty−∞ from other
Flip and flip the sign (reciprocal then negate)
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