MATH-M 211 Lecture 17: 3.9 Notes (Dec. 10)
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Rvw. - find the equation of the tangent line to at x = 2. Point of tangency- (2, -1: as long as close to point of tangency, tangent line mimics/approximates actual graph. Closer to point of tangency, more graph looks like tangent line, better approximation is- called linearization. Use linearization to complete linear approximation: in general, if point of tangency is , equation of tangent line is - point slope form. Solving for y gives or: always plug in known output [f(c)] to derivative- not unknown. If you cannot simplify the derivative without a perfect square, you made a mistake. Always build tangent line at known point- nearest perfect square. Find equation of tangent line at (16, 4)- point of tangency, then let x = 17: if exact decimal known, can convert from fraction form. If not known/messy fraction, leave as mixed or improper fraction: graph of f(x) Concave up tangent line below graph approximation less than actual.
