find exactly the taylor polynomial of degree 4 for

f(x) = e^(2x)

about x = -3

f(x) = e^2x e^-6

f'(x) = 2e^2x 2e^-6

f"(x) = 4e^2x 4e^-6

f"'(x) = 8e^2x 8e^-6

f""(x) = 16e^2x 16e^-6

right?

so to write it out its like

p4(x, -3) = e^-6 + (x-3)/1!*2e^-6 + (x-3)/2!*4e^-6 and so on is that right or since its -3 should it be

p4(x, -3) = e^-6 + (x+3)/1!*2e^-6 + (x+3)/2!*4e^-6

???