TAYLOR POLYNOMIALS AND ERROR IN TAYLOK SERIES Let f(x) = x4 + x3 + x2 + x + 1
(a) Use Taylor's Theorem to compute the remainder R 3 ( x ) in terms of value c that lies between 0 and x.
(b) Give an upper bound on the error assuming x∈ [ − 4 , 4 ].
(c) Compute the exact value of c (in terms of x) so that R 3 ( x ) = f ( x ) − p 3 ( x ) and R 3 ( x ) in part (a) agree.
Note: p 3 ( x ) is the 3rd-order Taylor polynomial.