Final answer:
The function g(x) = -3x^2 + 10x + 1 is increasing for x-values less than 5/3 and decreasing for x-values greater than 5/3.
Step-by-step explanation:
To determine the x-values for which the function g(x) = -3x^2 + 10x + 1 is increasing or decreasing, we need to find its vertex and analyze its slope. For a quadratic function in the form of ax^2 + bx + c, the vertex can be found using the formula -b/(2a). In this case, a = -3 and b = 10, so the vertex x-value is -10/(2*(-3)) = 5/3.
Since the coefficient of x^2 is negative, the parabola opens downward. This indicates that the function g(x) is increasing on the interval (-∞, 5/3) and decreasing on the interval (5/3, +∞).