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Unformatted text preview: EE 231_B1 Damir Iraliyev 1246540 Homework#5: Question7.4 Given a function =- . + + fx 1 5x6 2x4 12x a) Plot the function b) Use analytical Methods to prove that the function is concave for all values of x c) Differentiate the function and then use root-location method to solve for the maximum f(x) and corresponding value of x Solution: a) For Graph of f(x) please refer to the back of this report. Thank you. b) A continuous function is said to be concave if and only If a function always bears negative results for second derivative of the function therefore the function is concave: We check and see: =- . + + fx 1 5x6 2x4 12x =- + + f'x 9x5 8x3 12 =- + f''x 45x4 24x2 As we can clearly see from f(x) that the function is always negative for all values of x because of the x^4 and x^2 and the fact that -45>24. QED c) First derivative of the function is: =- + + f'x 9x5 8x3 12 And =- + f''x 45x4 24x2 Then we use Newton-Raphson Method to locate the root of the function since we positively know that the function is convergent? We select a starting point possibly close to the real value which we guess as x=1.2 So we begin: Iteration I) xi=1.2...
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This note was uploaded on 12/20/2010 for the course E E 231 taught by Professor Vorobyov during the Spring '10 term at University of Alberta.
- Spring '10