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b) The graph of a function f is given in Figure 1. Use it to sketch the derivative function, f'. [4] Figure 1 C) Two vertical poles PO and ST are secured by a rope RPS going from the top of the first pole to a point R on the ground between the poles and then to the top of the second pole as in Figure 2. Show that the shortest length of such a rope occurs when 0, = 02. R T(i) Obtain the fifth-order Taylor series for e about x=0.b) Sketch a possible graph of a function that satisfies the following conditions. Explain the information conveyed by each condition. (i) f(0) =0, f(2) =3, f(4)=6, f'(0) = f'(4)= 0 (ii) f'(x)>0 for 0 4 (iii) f"(x) > 0 for x 2 C) A piece of wire 10m long is used to form a square and an equilateral triangle. Find the dimensions, which give a minimum area.The error function erf ( xx ) = erdt 0 is used in probability, statistics and engineering. Show that the function y = ex erf (x) satisfies the differential equation y' = 2xy+2/Jm