Final answer:
The maximum value of the function f(x) = -3x² + 6x is achieved at x = 1.
Step-by-step explanation:
The equation f(x) = -3x² + 6x represents a quadratic function. To find the maximum value of the function, we can use the formula for the x-coordinate of the vertex. The x-coordinate of the vertex is given by x = -b/(2a), where a, b, and c are the coefficients of the quadratic function.
In this case, a = -3 and b = 6. Plugging these values into the formula, we get x = -6/(2*(-3)) = -6/(-6) = 1.
Therefore, the maximum value of the function f(x) = -3x² + 6x is achieved at x = 1.