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Question
Use the linear approximation to find approximate values of `(123)^(2/3)`
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Solution
Let x0 = 125, Δx = – 2
f(x) = `x^(2/3)`, f(x0) = 25
We know that
f(x0 + Δx) = f(x0) + f'(x0) Δx
`(123)^(2/3) = 25 + 2/(3x^(1/3)) (- 2)`
= `25 + 2/(3(125)^(1/3)) (- 2)`
= `25 + 2/(3 xx 5) xx - 2`
= `25 - 4/15`
= 25 – 0.2666
`(123)^(2/3)` = 24.7334
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