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Question 6 - Find Minimum & Maximum f8 marks Determine all LOCAL maximum and minimum points of ONLY TWO of the following. State whether each is a maximum or a minimum. 2x4 xe c) for) d)f(x) = 25:in x/x,over [ 1t,1t] {4 marks Note the correction for 6d) : as should not be under the root! {4 marks Question 7 - Estimate Roots 1 5 marks In this investigation you will explore a technique for estimating the solution to an equation (e.g. when finding a root). Use Newton's method to provide a solution to ONLY ONE of the following: b) Find the solution to the following function to 2 decimal places. Start with an initial guess of x = 0 2x - 1 = sin x 1 5 marks Newton's Method of Finding Roots To estimate a solution, say x = r to the equation f (x) = 0, following the steps below repeatedly. 1. Begin with an initial guess X (It would be great to pick a guess that is close to the solution.) f ( x] ) 2. Calculate (a better guess) X, = X1 - F(x,) f ( x , ) 3. If X is known then X n+1 =x n f ( x ) n 4. If x and x n+ agree to K decimal places, then X approximates the root r up to k decimal places and f (x ) ~ 0. Watch the following clips if the above steps are still not clear to you. https://youtu.be/comAk82cr9M https://youtu.be/ER5B_YBFMJo