Find Intervals of Increase and Decrease: y = -(x - 1/3)² + 4

The given quadratic function is $y = -\left(x - \frac{1}{3}\right)^2 + 4$. This is in vertex form, where the vertex is $\left(\frac{1}{3}, 4\right)$ and the coefficient $a = -1$ indicates the parabola opens downward.

For a downward-opening parabola, the function decreases immediately after the vertex and increases before it. Thus, we identify:

• The function is increasing for $x < \frac{1}{3}$.
• The function is decreasing for $x > \frac{1}{3}$.

Therefore, the intervals of increase and decrease of the function are:

$\searrow: x > \frac{1}{3}$ (decreasing) $\nearrow: x < \frac{1}{3}$ (increasing)

The correct answer, corresponding to the choices given, is:

$\searrow:x>\frac{1}{3}\\\nearrow:x<\frac{1}{3}$