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ee231_HW5

ee231_HW5 - EE 231_B1 Damir Iraliyev 1246540 Homework#5...

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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?

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ee231_HW5 - EE 231_B1 Damir Iraliyev 1246540 Homework#5...

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