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3.7 Differentials p. 267

Explore how tangent lines can be used to approximate function values and learn about differentials as another alternative for approximation. Discover the concept of linearization and its application in finding excellent approximations when close to a given point.

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3.7 Differentials p. 267

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  1. 3.7Differentialsp. 267

  2. Tangent lines can be used to approximate function values.

  3. Tangent line approximation *also called a linear approximation or the linearization of a function. *can yield excellent approximations of f if sufficiently close to c.

  4. Differentials – another method of approximating dx=Δx=change in x dy= amount tangent line rises/falls. Δy=amount actual curve rises/falls.

  5. AP Example If a square with a side length of “e” is increased 1%, what is the approximate increase in area?

  6. Homework p. 272 1, 9, 50-53 all

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