A graph of f(ac) = ac" + 3ac -40x - 90 shows that the equation a" + 3x - 40x - 90 = 0 will have a solution on the interval (6, 7). Use Newton's method, showing at least the first cycle of the process, with initial approximation co = 6.5 to approximate the solution of a + 3xc - 40x - 90 - 0. Stop when the solution is accurate to four decimal places, and report the solution accurate to four decimal places. Solution: * ~Consider the function f(x ) = x8 + 10x4 + 11x - 80. A. Verify that f(x) = a + 10x + 11x - 80 satisfies the hypotheses/ conditions of the Mean Value Theorem on [2, 3]. {Show the work/reasoning for this part on paper.} B. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem (to three decimal places). C~A cardboard box with an open top must have a volume of 14 fto. If the length of the base is two times the width of the base, determine the dimensions of the box that will minimize the amount of cardboard used. [You may round the dimensions to three decimal places.] height width length Width: ft Length: ft Height: ft