Problem 4. Consider the function

f:R->R

defined by\

f(x)=\\\ oot(3)(x)

\ Find a formula for

f^((n))(x)

, for all

n

. Write the third Taylor polynomial

P_(3)(x,8)

for

f

\ about 8 .\ Find the smallest

n

for which you are sure that

P_(n)(9,8)

approximates

\\\ oot(3)(9)

with an\ error smaller than

(1)/(1000)=0,001

.\ [1 point]

Problem 4. Consider the function f:RR defined by f(x)=3x. 1. Find a formula for f(n)(x), for all n. Write the third Taylor polynomial P3(x,8) for f about 8 . 2. Find the smallest n for which you are sure that Pn(9,8) approximates 39 with an error smaller than 10001=0,001. [1 point]