Please help me with the below question. Question 2 Consider the function f: [-1, 1] → Rf(x) = (x - 1)ª ln(x²+x+1),where a, b are the last two digits of your student number, which are greater than 1. The shape of thefunction is complicated enough that it is hard to draw using hand calculations. You will use Taylorpolynomials to approximate different parts of the function to estimate the shape of its graph and toapproximate some stationary points. If you wish you can use a graphing calculator or an app or website to see the computed shape of the graph, however, this is not necessary and your answer shouldcontain only information you have calculated below, not information from another source. It is fineto use a normal calculator if you need to find the decimal expression of a value to plot it.(a) Write down f(x) for your a and b (and use it for this and the remaining questions). Calculatethe first and second derivatives f'(x) and f"(r) (no need to simplify the expressions).(b) Calculate the three different second-order Taylor polynomials (T₂f) (r) centred around threex-values: x= -1, z = 0 and a = 1. Show all working.(c) Either by hand, or by using a computer program, draw the three graphs of second-order Taylorpolynomials determined in (b), in one figure.(d) Recall that a Taylor polynomial is a good approximation close to the point it is centred around,but often a bad approximation away from that point. You will be asked (e) to sketch, by hand,the approximate shape of the graph of f(x). However, you are allowed to calculate the valueof f at two chosen values of z. Based on the graphs of (c), what values would you choose?Explain why, and provide the value of f at those points.(e) Using (d), sketch, by hand, the approximate shape of the graph of f(x) between x = -1 andx = 1, in the same figure as in (c). Use a different colour or different style (e.g. dashed) todistinguish it from the Taylor polynomials you have drawn.20433209 this is student number (Need Asap)

Question

Please help me with the below question. Question 2 Consider the function f: [-1, 1] → Rf(x) = (x - 1)ª ln(x²+x+1),where a, b are the last two digits of your student number, which are greater than 1. The shape of thefunction is complicated enough that it is hard to draw using hand calculations. You will use Taylorpolynomials to approximate different parts of the function to estimate the shape of its graph and toapproximate some stationary points. If you wish you can use a graphing calculator or an app or website to see the computed shape of the graph, however, this is not necessary and your answer shouldcontain only information you have calculated below, not information from another source. It is fineto use a normal calculator if you need to find the decimal expression of a value to plot it.(a) Write down f(x) for your a and b (and use it for this and the remaining questions). Calculatethe first and second derivatives f'(x) and f&#34;(r) (no need to simplify the expressions).(b) Calculate the three different second-order Taylor polynomials (T₂f) (r) centred around threex-values: x= -1, z = 0 and a = 1. Show all working.(c) Either by hand, or by using a computer program, draw the three graphs of second-order Taylorpolynomials determined in (b), in one figure.(d) Recall that a Taylor polynomial is a good approximation close to the point it is centred around,but often a bad approximation away from that point. You will be asked (e) to sketch, by hand,the approximate shape of the graph of f(x). However, you are allowed to calculate the valueof f at two chosen values of z. Based on the graphs of (c), what values would you choose?Explain why, and provide the value of f at those points.(e) Using (d), sketch, by hand, the approximate shape of the graph of f(x) between x = -1 andx = 1, in the same figure as in (c). Use a different colour or different style (e.g. dashed) todistinguish it from the Taylor polynomials you have drawn.20433209 this is student number (Need Asap)

Accepted Answer

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