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

$\begin{array}{rl}{T}_2(x)& =f(1)+f^{\prime }(1)(x-1)+f^{″}(1)(x-1{)}^2/2\\ & =1+(0)(x-1)+(-2)(x-1{)}^2/2\\ & =1-(x-1{)}^2\\ & =-x^2+2x\\ & =x(2-x)\end{array}$

The graph is given below.