Final answer:
The slope of the tangent line to the graph of f(x) = x³ - 6x + 3 at the point (0, 3) is found by evaluating the derivative f'(x) = 3x² - 6 at x = 0, which is -6.
Step-by-step explanation:
The question asks for the slope of the tangent line to the graph of the function f(x) = x³ - 6x + 3 at the point (0, 3). To find the slope of the tangent, we need to calculate the derivative of the function, f'(x), and then evaluate it at x = 0.
The derivative of f(x) is f'(x) = 3x² - 6. Now, substituting x = 0 into f'(x), we get f'(0) = 3(0)² - 6 = -6. Therefore, the slope of the tangent line at the point (0, 3) is -6, which corresponds to option d.