Problem 4 [15 points]. Write a Matlab program that implements the steps outlined in Problem 2.7. Use your algorithm to compute the minimum that appears between x = 1 and x = 2 of the function f(x) = ( /x) + sinh[ln(x^2 + 2)] .

u0u0OS ile llcessary till we converge to the root, r =-0i/T, of f(x) ? P2.7. The bisection algorithm is an iterative scheme for finding the root of an equation f(x) = 0, Let's apply this same methodology in finding the minimum of a function y = f(x). Consider the function y = f(x) sketched in Figure 2.22, between xleft and xright there is a unique local minimum, a. We can be sure that there is a local minimum between Teft and Tright because f(tleft) > f(zmid) and f(xright) > f(zmia) where arni.- (2)eft + Xright). From this starting point, outline the steps required to converge to the local minimum, a*, of f. Hint: Consider the value of r that is mid-way between Teft and Tmid and also the value of r that is mid-way between Tmid and Tright. Based on the value of the function at these points, you should be able to shrink the interval bracketing a and possibly update your estimate of as well. P2.8. Consider the three-loop electrical circuit shown schematically in Figure 2.23. By summing the voltage drops around each of loops 1, 2 and 3, it can be shown that (2.19) (2.20) -ti Ri + i2(R1 + R3 + R4)-23R4 =