Please help with the following questions:

2. Which of the functions graphed in the following figure is most likely to have P(x) = 6-x + 2x2 as its second-order Maclaurin polynomial? IV3. 14. Let P(x) = 3- 3x2 + 6x* be the fourth-degree Taylor polynomial for the function f about x = 0. What is the value of f() (0) ? (A) 0 (B) (C) 6 (D) 24 (E) 144 4. 11. The third-degree Taylor polynomial for a function f about x = 4 is (* -4) _(x-4)" (x-4) + 2. What is the value of f"(4) ? 512 64 4 (A) -1 64 (B) . 1 (C) 1 32 (D) 3 512 81 256 (E) 256 5. 86. The Taylor polynomial of degree 100 for the function f about x = 3 is given by P(x ) = (x - 3)2 _ (x - 3) (x-3)6 - + ... + (-1)2+1 (x -3)2n - + .... (x - 3)100 2! 3! n! 50! . What is the value of f(30) (3) ? (A) 30! 15! (B) (C) (D) 1 30! 30! 15! (E) 30! 15!6. 6. A function f has derivatives of all orders at x = 0. Let Pr (x) denote the nth-degree Taylor polynomial for f about x = 0. (a) It is known that f(0) = -4 and that Piz = -3. Show that f'(0) = 2. (b) It is known that f"(0) = -2 and f"(0) = 2. Find P3(x). (c) The function h has first derivative given by h'(x) = f(2x). It is known that h(0) = 7. Find the third-degree Taylor polynomial for h about x = 0. 7. Consider the logistic differential equation - dy _ y dt (6 - y). Let y= f(t) be the particular solution to the differential equation with f(0) = 8 Write the second-degree Taylor polynomial for fabout t = 0, and use it to approximate f(1)