Consider the following unconstrained non linear optimisation problem: maxf(x)=2x4+28x3120x2+140x. We are interested in_solutions in the interval [0,2]. We would like to find the maximum with an absolute error below 0.3. (a) Find the length of the initial interval and the number of iterations to approximate the maximum using the golden ratio method. [5 marks] (b) Carry out the iterations of the golden ratio method to approximate the maximum. [15 marks] Consider the following unconstrained non linear optimisation problem: maxf(x)=2x4+28x3120x2+140x. We are interested in_solutions in the interval [0,2]. We would like to find the maximum with an absolute error below 0.3. (a) Find the length of the initial interval and the number of iterations to approximate the maximum using the golden ratio method. [5 marks] (b) Carry out the iterations of the golden ratio method to approximate the maximum. [15 marks]