Posted by PAUL on .
Let f(x) = 3(x-1)^3 + 4(x-1)^2 + 2(x-1) -7
(a) Determine f'''(1) without taking any derivatives. Explain your method.
(b) Determine the general Taylor polynomial of f aobut c =2 by computing any for each k, using the formula above for f(x).
(a) Only the first term (3x-1)^3, will have a nonzero third derivative, and it will be the derivative of the 3x^3 term, which is 3*3! = 18
(b) You have not defined k. Is it the different exponents of the (x-1) terms?