Find the Domain of Increase: y = 3x² - 6x + 4 Quadratic Function

The function given is $y = 3x^2 - 6x + 4$.

First, let's find the derivative of the function, which will help us determine the intervals of increase.

The derivative is given by $f'(x) = \frac{d}{dx}(3x^2 - 6x + 4) = 6x - 6$.

Next, find where the derivative is zero to locate critical points. Solve $6x - 6 = 0$ to get:

$6x = 6$
$x = 1$

The critical point is $x = 1$. This is where the function changes from decreasing to increasing since quadratic functions have one axis of symmetry and $a > 0$: indicating a parabola opening upwards.

To determine the interval of increase, analyze the sign of $f'(x)$:

• For $x > 1$, $6x - 6 > 0$ which implies $f'(x) > 0$, so the function is increasing.
• For $x < 1$, $6x - 6 < 0$ which implies $f'(x) < 0$, so the function is decreasing.

Thus, the domain of increase for the function is when $x > 1$.

The correct answer is therefore $x > 1$.