EGR_102_Lecture_10_HW_Solution

EGR_102_Lecture_10_HW_Solution - EGR 102 Lecture 10 HW This...

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EGR 102 of 2 pages Lecture 10 HW 1 EGR 102 Lecture 10 HW This lecture homework will not be collected nor graded This material will be on Lecture Exam 2 Name: Solution PID: Lab Section #: Problem 1: Using Excel or MATLAB, plot the function given below and then use Newton’s method to determine its maximum value. Use an initial guess of x 0 = 2 and perform 5 iterations using 4 decimal places. Place your answers in the spaces provided. f(x) = – 1.5x 6 – 2x 4 + 12x i x f(x) f'(x) f"(x) 0 2.0000 -104.0000 -340.0000 -816.0000 1 1.5833 -17.2029 -109.3126 -342.9813 2 1.2646 3.9246 -33.2898 -153.4765 3 1.0477 8.1786 -8.5628 -80.5683 4 0.9414 8.6818 -1.3309 -56.6200 5 0.9179 8.6979 -0.0528 -52.1708 The first and second derivatives of the function can be evaluated as: 12 8 9 ) ( ' 3 5 x x x f & 2 4 24 45 ) ( " x x x f which can be substituted into Newton’s equation to give: 2 4 3 5 1 24 45 12 8 9 i i i i i i x x x x x x Substituting the initial guess yields:
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EGR_102_Lecture_10_HW_Solution - EGR 102 Lecture 10 HW This...

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