The third degree Taylor polynomial of f around x=2 is...
T(x) = 7 - 9(x-2)^2 - 3(x-2)^3
The fourth derivative satisfies the inequality [abs(f''''(x))] <_ 6 for all x in the closed interval [0,2]. Use the Lagrange error bound on the approximation of f(0) via T(0) to explain why f(0) is negative.