Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places.)
3 cube root26
using differentials
using a calculator
I will assume that you are familiar with
f(x + ∆x) = appr = f(x) + dy = f(x) + f ' (x)dx
let f(x) = y = 3x^(1/3)
dy/dx = x^(-2/3)
dy = x^(-2/3) dx
f(26) = f(27 - 1)
in our case x = 27 and ∆x = -1
= appr f(27) + 27(^-2/3)(-1)
= 9 - 1/27^(2/3)
= 9 - 1/9
= 80/9 = 8.8889 correct to 4 decimals
by calculator 3(26)(1/3) = 8.8875