Giving a precise mathematical description of natural phenomenon can be quite difcult. It is often more practical for scientists and engineers to describe nature by looking for relations among how it changes. In certain situations, Taylor polynomials can be used to approximate functions without an explicit description. Consider a function f(t). It is known that it satises the following conditions: f"(t) = N): f(1) = 0, f'(1)= 1- We also know |f(t)| and |f'(t)| are bounded above by 3H1 over the interval [0,2]. (a) Compute Taylor polynomial of degree 3 for f (t) centred at 1. (b) Using information available, what is the lowest degree Taylor polynomial for f (as) centred at 1 to guarantee an approximation of f (2) to an absolute error to within 0.001