Use linear approximation

Question

use linear approximation of the function f(x)=³√x at x=8 to estimate the value of ³√8.06

Answer 1

Start with y = x^(1/3) then dy = (!/3)x^(-2/3) dx

if x = 8, and dx = .06 then dy = (1/3)(8)^(-2/3)(+.06) = +.005

So, (8.06)^(1/3) is approximately equal to 8.005