Science:Math Exam Resources/Courses/MATH104/December 2012/Question 06 (d)/Solution 1

Plugging in the values from part (a) and part (b) into the second degree Taylor polynomial (recalling the a value is 1) gives

${\begin{aligned}T_{2}(x)&=f(1)+f'(1)(x-1)+f''(1)(x-1)^{2}/2\\&=1+(0)(x-1)+(-2)(x-1)^{2}/2\\&=1-(x-1)^{2}\\&=-x^{2}+2x\\&=x(2-x)\end{aligned}}$

The graph is given below.