Function g is twice differentiable at x=1. A quadratic polynomial P(x)=a+b(x−1)+c(x−1)2 is chosen to approximate g near x=1. Which of the following equalities must hold if and only if P shares the same slope as g at x=1?
a) P(1)=g(1)
b) P′′(1)=g′′(1)
c) P′(1)=g′(1)
d) P′(1)=g(1)