Question

Find the degree 3 Taylor polynomial T3(x) of the function f(x)=(7x+50)4/3 at a=2

Find the second-degree Taylor polynomial for f(x)=4x2−7x+6 about x=0

thank you! (:

Answer 1

Taylor's series about a (to x² term):
f(x)=f(a) + f'(a)x/1! + f"(a)x²/2!

For
f(x)=(4/3)(7x+50)=(28x/3)+200/3, and a=2
f'(x)=28/3
f"(x)=0

f(x)=f(2) + f'(2)(x-2)/1! + f"(2)(x-2)²/2!
=(4/3)(64) + 28/3(x-2) + 0(x-2)²/2!
=(4/3)(7x-50)

Try the second one along the same lines, and post if you would like to check the answer, which should be the same as the original function.