Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.
$f ( x ) = 6 x ^ { 2 } - 12 x + 6$
A) increasing on (-$\infty$, $\infty$)
B)descreasing on (-$\infty$, 1)increasing on (1, $\infty$)
C) increasing on (-$\infty$, 1)descreasing on (1, $\infty$)
D) descreasing on (-$\infty$, $\infty$)
E)descreasing on (1, 1)increasing on (1, $\infty$)

Question

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. 
 $f ( x ) = 6 x ^ { 2 } - 12 x + 6$  
A) increasing on (-$\infty$, $\infty$)
B)descreasing on (-$\infty$, 1)increasing on (1, $\infty$)
C) increasing on (-$\infty$, 1)descreasing on (1, $\infty$)
D) descreasing on (-$\infty$, $\infty$)
E)descreasing on (1, 1)increasing on (1, $\infty$)

Quizplus · Accepted Answer

The function $f(x) = 6x^2 - 12x + 6$ is a quadratic function with a positive leading coefficient (6), indicating that it opens upwards. The vertex of this parabola, found by using the formula $-\frac{b}{2a}$, is at $x = 1$. This means the function is decreasing before $x = 1$ and increasing after $x = 1$.

Use a Graphing Utility to Graph the Function and Visually f(x)=6x2−12x+6f ( x ) = 6 x ^ { 2 } - 12 x + 6f(x)=6x2−12x+6

Use a Graphing Utility to Graph the Function and Visually $f ( x ) = 6 x ^ { 2 } - 12 x + 6$