A twice–differentiable function g is represented near a point by the polynomial
P(x)=7−5(x−4)+3(x−4)2.
Assume P is the Taylor polynomial of least possible degree that matches g at the appropriate point.
(a) Identify the value of x about which P is centered.
(b) State the degree of P.
(c) Describe, in complete sentences, how the structure of P leads to your answers in parts (a) and (b).