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PROBLEM 5.12 and more!. points 50 { Use MATLAB Consider the function: f(x) = 2x^6 - 1.5x^4 + 10x + 2 Determine the maximum of this function by employing the following tasks: a. Plot in Matlab the f(x) in a range of x that includes its maximum value. Make sure you can see it! b. After identifying the maximum and its location at xmax graphically, determine which function F(x) to use in order to nd xmax as a root of that function. c. Use the buit-in Matlab command fzero to nd xmax as a root of F(x); look at the documentation how to use it! Use as initial guess either of xl or xu. CAUTION: which function are you using? d. Use the Newton-Raphson method to nd xmax as a root of F(x). Choose an appropriate initial guess x0. Compute both the true and approximate errors. As true value of the root use the one you obtained in question (c). Use as stopping criteria the error tolerance s = 1*10^6 and a maximum number of 50 iterations. Present your results in a table similar to that of example 5.4, page 130 of textbook. You should use the function myNewton you developed in Problem 1. e. Use the Secant method to nd xmax as a root of F(x). Choose appropriate initial guesses x(-1) and x0. Compute both the true and approximate errors. As true values of the root use the one you obtained in question (c). Use as stopping criteria the error tolerance s = 1*10^6 and a maximum number of 50 iterations. Present your results in a table similar to that of example 5.4, page 130 of textbook. You should use the function mySecant you developed in Problem 2. f. Use the bisection and false-position methods to nd xmax as a root of F(x). Choose appropriate initial guesses xl and xu that bracket the root. Compute both the true and approximate errors. As true values of the root use the one you obtained in question (c). Use as stopping criteria the error tolerance s = 1*10^6 and a maximum number of 50 iterations. Present your results in a table similar to that of example 5.4, page 130 of textbook. You should use the functions myBisection and myFalsePosition you developed in Programming Assignment 5. g. Plot in a common gure (semi-logarithmic on the y-axis) the true and approximate relative percent errors et; ea you obtained with the Newto-Raphson, the Secant, the Bisection and the False-Position methods in questions (d), (e) and (f). Hint: provide a graph similar to Fig. 5.13, page 137 of your textbook. h. Comment on the results and graphs of the previous questions. Make suggestions for improvement of the solutions if not satisfactory.

PROELEM 5.12 ard more!. Points -Use MATLAB Conider the functicn: Determire the maimue of this functin by eploying the follbwing tsk: Plot in Matkab the fer) in .range of you cn see it that includes its rearoun wahe. Male sure b. Ater identityng the mmcim nd it location at gphially detecine which function Fes) to use in order to fud n0%-.mot of the function.. e. Use the buit-in Matlab ooraraand fzero to find root of F(100k at the either of or, CAUTION: which docucethtion how to use it s funetion sre you ng? initia] d. UetheNewton-Raphson method to findFotof F). Choose nappmpriate initial sueCompute both the true nd opponate erors. As true vlue of tle root use the one you obtained in ques wn (:)Useas stopping ontenathe emor tolerance ,-1 x 10-'snd rearoun nunber of 50 iterations. Pr-sent your results i "table sinribr to that ok aerple 54, poge 130 of tertbook. You should use the iunction myHovton you devebped in blem 1. e. Use the Seco nt method to find mx3f root of F(r). Choose appropr ate initial guesses -1 ndCopite both the true ond eppmircote erors. As true olu of the root use the oneu obtied in question (c). Ue e stopping criter. the error tolernce e, 1 10 ndiou nmber of 50 iterations. rse ults in tabe sincibr to that ok eorple 54, poge 130 of tertbook. You should use the fiunction msocat you devebped in ble 2. f. Use the bisection and false-position rethods to find max \ .mot o F( ). Chocee approprbte initi I guesses and that bra let the root. Compute both the true and ppronimate e As true lues of the root use the one you obtined in questicn (c). Ue s stopping cniteria the erwr toernce e, 1 10* ond rdrcoumber of 50 itentions. Freent yourruts in table similar to that ofepe 5.4 pge 130 of tertbook. You should use the functions myBisoction nd nyFslsoPosition y developed in grning Asignmerd 5. s. Plot in coaon figure era-bgrithmic on they-i) the true ad pptreltive percert er t you obtained with the lNwto-Fpkon, the Secont, the Eiectionnd the FiseFosition ethods in quertions (d (e) and (f). Fit pd agasito h. Connert on the reulte ond gnphs of the prvionus quetions. Make suggetions for ircpovrent of the solitions ifnotstitory PROELEM 5.12 ard more!. Points -Use MATLAB Conider the functicn: Determire the maimue of this functin by eploying the follbwing tsk: Plot in Matkab the fer) in .range of you cn see it that includes its rearoun wahe. Male sure b. Ater identityng the mmcim nd it location at gphially detecine which function Fes) to use in order to fud n0%-.mot of the function.. e. Use the buit-in Matlab ooraraand fzero to find root of F(100k at the either of or, CAUTION: which docucethtion how to use it s funetion sre you ng? initia] d. UetheNewton-Raphson method to findFotof F). Choose nappmpriate initial sueCompute both the true nd opponate erors. As true vlue of tle root use the one you obtained in ques wn (:)Useas stopping ontenathe emor tolerance ,-1 x 10-'snd rearoun nunber of 50 iterations. Pr-sent your results i "table sinribr to that ok aerple 54, poge 130 of tertbook. You should use the iunction myHovton you devebped in blem 1. e. Use the Seco nt method to find mx3f root of F(r). Choose appropr ate initial guesses -1 ndCopite both the true ond eppmircote erors. As true olu of the root use the oneu obtied in question (c). Ue e stopping criter. the error tolernce e, 1 10 ndiou nmber of 50 iterations. rse ults in tabe sincibr to that ok eorple 54, poge 130 of tertbook. You should use the fiunction msocat you devebped in ble 2. f. Use the bisection and false-position rethods to find max \ .mot o F( ). Chocee approprbte initi I guesses and that bra let the root. Compute both the true and ppronimate e As true lues of the root use the one you obtined in questicn (c). Ue s stopping cniteria the erwr toernce e, 1 10* ond rdrcoumber of 50 itentions. Freent yourruts in table similar to that ofepe 5.4 pge 130 of tertbook. You should use the functions myBisoction nd nyFslsoPosition y developed in grning Asignmerd 5. s. Plot in coaon figure era-bgrithmic on they-i) the true ad pptreltive percert er t you obtained with the lNwto-Fpkon, the Secont, the Eiectionnd the FiseFosition ethods in quertions (d (e) and (f). Fit pd agasito h. Connert on the reulte ond gnphs of the prvionus quetions. Make suggetions for ircpovrent of the solitions ifnotstitory