use linearization to approximate the value of ³√7.89

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beckden eNotes educator| Certified Educator

`root(3)(8) = 2` so we will linearize around that number.

`y = root(3)(x)` `y' = 1/3 x^(-2/3)` So at x=8 we have `y'=1/3(8)^(-2/3) = 1/3(2)^(-2) = 1/12` so linearization is `y=1/12(x-8)+b` At x=8 y=2 so b=2 So `y = 1/12(x-8)+2` .  At x=(7.89) we get `y=1/12(-0.11)+2 = -0.009166...` So y `~~` 1.990833 Actual value `~~` 1. 99079100  so our estimate is good to 3 decimal places.