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Linear approximation

Use linear approximation, the tangent line approximation, to approximate the following:

(56.4)^(1/3)

(64.4)^(1/3)

Show processes.
Do not use a calculator.
Note: the correct answer are different from the calculator computed values

Solution Preview

[1] to approximate (56.4)^{1/3} let f(x) = x^{1/3} and pick a = 64 so that f(a) = 4 and let x = 56.4;
then x - a = 56.4 - 64 = -7.6 = - 38/5, ...

Solution Summary

This shows how to use linear approximation to approximate decimals to a given power.

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