Let f be a function having derivatives of all orders for all real numbers. The third-degree Taylor polynomial for f is given by P(x) = 4+3(x+4)^2 - (x+4)^3 a) Find f(-4), f"(-4), and f'"(-4). b) Is there enough information to determine whether f has a critical point at x=-4? If not, explain why not. If so, determine whether f(-4) is a relative maximum, a relative minimum, or neither, and justify your answer c) Use P(x) to find an approximation for the y-intercept for f . Is there enough information to determine whether f has a critical point along the y-axis? If not, explain why not. If so, determine whether the critical point is a relative maximum, a relative minimum, or neither, and justify your answer. d) The fourth derivative of f satisfies the inequality |f^(4) (x)| ≤ 11/10 for all x in the interval (-4,0]. Use the Lagrange error bound on the value of the y-intercept found in part c) above to explain why the y-intercept must be negative.