Final answer:
Upon evaluating the function f(x) = x^4 + 4x^3 + 4x^2 + 14x + 1 at x = -4, the result is 9. This does not match any of the provided options, which suggests there may be an error in the question itself.
Step-by-step explanation:
To evaluate the function f(x) = x^4 + 4x^3 + 4x^2 + 14x + 1 at x = -4, we substitute -4 into the function and calculate the result:
f(-4) = (-4)^4 + 4(-4)^3 + 4(-4)^2 + 14(-4) + 1
= 256 - 256 + 64 - 56 + 1
= 256 - 256 + 64 - 55
= 0 + 64 - 55
= 64 - 55
= 9
Therefore, the result of evaluating the function at x = -4 is 9, which is not one of the options provided. There must have been a mistake in the question, as none of the given options (a) -383, (b) 383, (c) 0, (d) 49 match the evaluated result of 9.