The Bisection Method is a rootfinding algorithm that can be conducted on a continuous function to find the root up to a given error as follows: 1. Find (or be given} an :31 and :52 such that Intermediate Value Theorem guarantees that m] = 0 on (x1, x2}. :1: + a? 2. Bisect your interval by finding the midpoint 1:3 2 1T2. 3. Evaluate f[a:3). 4. Use IVT to determine if the root is in the interval ($1, $3) or [9:3, 3:2}. 5. Repeat steps 24 until half the length of your determined interval in step 4 is less than the error you have been provided. Thenr the midpoint ofthis determined interval is your approximated root location within the given error. Now, given the function x) 2 $3 l 53:2 :3 5 and the initial interval [7, 2]: a) Show that the IVT guarantees a root on (77, 72) (so that step 1 is satisfied). b) Conduct the Bisection Method to approximate the root location (in either exact fractional or decimal form) of Km} with a maximum error of 0.4