Question

No Calculator Let gbe a twice-differentiable function. The function g and its derivatives have the properties indicated in the table above. 0 0​

Answer 1

Hi there!

Part D:

We can use the Taylor Polynomial expansion for a second-degree polynomial:

`P_3(x) = g(c) + (g'(c))/(1!)(x - c) + (g''(c))/(2!)(x - c)^2`
Where c is the value that the polynomial is centered about.

We are given that:

`g(c) = 1\\\\g'(c) = 0\\\\g''(x) = 2`

Therefore:

`P_3(x) = 1 + (0)/(1)(x - 2) + (2)/(2!)(x - 2)^2\\\\\boxed{P_3(x) = 1 + (x - 2)^2}`