Tutorial10_Nov29.pdf - MATH1025 Introduction to Mathematics...

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MATH1025 Introduction to Mathematics and StatisticsIn-class exercises/Section 2/November 29NAME:STUDENTID:Question 1: The graph below represents the derivative,f0(x)(1) On what interval is the originalfdecreasing?(2) At which labeled value ofxis the value off(x) a local minimum?(3) At which labeled value ofxis the value off(x) a local maximum?1
Question 2: Letf(x) = 2x3-9x2+ 12x+ 1.(1) Find the critical points forf(x).(2) Determine the intervals of increase and decrease forf(x).(3) Use second derivative to determine local minimums and maximums.2
Question 3:(1) Use Newton’s method to find the real root off(x) =x3+ 5x-8. Start with the valuex0= 1.Please perform 4 iterations (getx4), and correct to 5 decimal places at each iteration.(2) By substituting your answer to part (a) intof(x) =x3+ 5x-8, comment on the accuracy of yoursolution tof(x) = 0.3
Question 4:(1) FindRx12dx.(2) FindR3x(6-x2)dx(3) FindR(x4+x+ 9)dx(4) FindR (-3x+ 3ex)dx.4
Solution:
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