My Calculus teacher gave me the following problem:
The function f has derivatives of all orders for all real numbers, and f^{(4)} (x) = e^{sin(x)}. If the third degree Taylor polynomial for f about x=0 is used to approximate f on the interval [0,1], what is the Lagrange error bound for the maximum error on the interval [0,1]?
My peers and I had a disagreement on the correct answer and I'm curious which one of us is right.