The nth Taylor polynomial for a function f at x0 is sometimes referred to as the polynomial

Question:

The nth Taylor polynomial for a function f at x0 is sometimes referred to as the polynomial of degree at most n that "best" approximates f near x0.
a. Explain why this description is accurate.
b. Find the quadratic polynomial that best approximates a function f near x0 = 1 if the tangent line at x0 = 1 has equation y = 4x − 1, and if f'' (1) = 6.