Question

Can somebody explain how to do part b for this?

Answer 1

apologies in advance for my calculus being rusty

but I believe you would just write


f(x) = f(x0) + f'(x0)(x-x0) + [ f''(x0)(x-x0)^2 ] / 2!
using the appropriate values from the table

Answer 2

for the approximation you'd just plug in x = 0.2 into the polynomial you just wrote and evaluate

Answer 3

I'm not super confident so I'm going to tag @imqwerty to look over this as well

Answer 4

Nvm I figured it out, all I had to do was plug in x^3 into the taylor polynomial to get
\[4 + 5x ^{3} - (x ^{3})^{2}/2!\]

Then differentiate it twice to get
\[15x ^{2}-3x ^{5}\]
Thanks for the help though!

Answer 5

np