Consider the Function $f ( x ) = 3 x ^ { 4 } - 24 x ^ { 3 } + 72 x ^ { 2 } - 96 x + 49$

question 29

Essay

Consider the function $f ( x ) = 3 x ^ { 4 } - 24 x ^ { 3 } + 72 x ^ { 2 } - 96 x + 49$ .(a) Find the fourth-degree Taylor polynomial of f at $a = 2$ .(b) What is the remainder?
(c) What is the absolute minimum value of f, and where does it occur?