Linear approximation
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Use linear approximation, the tangent line approximation, to approximate the following:
(56.4)^(1/3)
(64.4)^(1/3)
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Do not use a calculator.
Note: the correct answer are different from the calculator computed values
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Solution Summary
This shows how to use linear approximation to approximate decimals to a given power.
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[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, ...
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