Final answer:
The slope of the line tangent to the graph of f(x) = -3x² + 3x + 1 at x = 1 is -3.
Step-by-step explanation:
To find the slope of the line tangent to the graph of f(x) = -3x² + 3x + 1 at x = 1, we need to find the derivative of the function and evaluate it at x = 1.
First, we find the derivative of f(x) using the power rule for derivatives:
f'(x) = -6x + 3
Next, we evaluate the derivative at x = 1:
f'(1) = -6(1) + 3 = -3
Therefore, the slope of the line tangent to the graph of f(x) = -3x² + 3x + 1 at x = 1 is -3.