Compute the roots of function:
1. (15%) Consider the cubic polynomial function f(x) = x3 + x + 1. We know that this function is strictly increasing (i.e. if x1 < x2, then f(x1) < f(x2)).
a. (3%) Prove that this function is strictly increasing using differential calculus (Mat 114)
b. (12%) We know f(-1) = -1 – 1 + 1 = -1 < 0 and f(0) = 1 > 0. So from calculus, we know that there is a root (x0) such that f(x0) = 0 with -1 < x0 < 0. Write a computer program in C / C++ / C# / Python to calculate this root to at least 5 digits precision (do NOT use MATLAB’s root command). You may use algorithm like bisection, Newton etc.