Answer:
To find the slope of the line tangent to the graph of the function at x = -3, we need to find the derivative of the function and evaluate it at x = -3.
First, let's find the derivative of the function y = x^4 + 2x^3 + 2x + 2:
y' = 4x^3 + 6x^2 + 2
Now, let's evaluate y' at x = -3:
y'(-3) = 4(-3)^3 + 6(-3)^2 + 2
= -108 + 54 + 2
= -52
Therefore, the slope of the line tangent to the graph of the function y = x^4 + 2x^3 + 2x + 2 at x = -3 is -52.