Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places.)

Question

3root26 (que root)

using differentials
using a calculator

Answer 1

I did this same question a few days back, but with the "search" function
on this site not working at all, I can't find it.

Well, let's do it all over again.....

recall
f(x+ ∆x) = f(x) + f ' (x)*∆x

let f(x) = 3x^(1/3), I assume you meant 3cuberoot(26)
f ' (x) = x^(-2/3)

f(26)
= f(27 - 1) , here ∆x = -1
= f(27) + f ' (27)(∆x)
= 9 + 27^(-2/3)(-1)
= 9 - 1/9
= 8.8889 , correct to 4 decimals

actual answer using calculator: 3*26^(1/3) = 3(2.96249...)
= appr 8.8875

quite close