Find Intervals of Increase and Decrease for y = (x - 3 1/11)²

To solve this problem, we will analyze the quadratic function given in vertex form.

The function is $y = \left(x - 3\frac{1}{11}\right)^2$, which is in the form $y = (x - h)^2$. Here, $h = 3\frac{1}{11}$, which represents the vertex of the parabola.

For a quadratic function in the vertex form $y = (x - h)^2$:

• The function is decreasing on the interval $x < h$.
• The function is increasing on the interval $x > h$.

Because the function opens upwards (as the coefficient of $(x - h)^2$ is positive), it decreases on the left side of the vertex and increases on its right side.

Therefore, based on the vertex $x = 3\frac{1}{11}$:

- The function is decreasing for $x < 3\frac{1}{11}$. - The function is increasing for $x > 3\frac{1}{11}$.

Thus, the intervals you are looking for are:

$\searrow:x<3\frac{1}{11}\\\nearrow:x>3\frac{1}{11}$

Comparing this result to the given choices, the correct choice is:

Choice 3: $\searrow:x<3\frac{1}{11}\\\nearrow:x>3\frac{1}{11}$