The linear and quadratic approximations of a function f at x = a are P₁(x) = f′(a)(x − a) + f (a) and P₂(x) = 1/2 f ″(a)(x − a)² + f′(a)(x − a) + f (a).

(a) Find the specified linear and quadratic approximations of f,

(b) Use a graphing utility to graph f and the approximations,

(c) Determine whether P₁ or P₂ is the better approximation, and

(d) State how the accuracy changes as you move farther from x = a.

f(x) = tan x; a 4