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 (-?,?)
B)descreasing on (-?,1) increasing on (1,?)
C)?increasing on (-?,1) descreasing on (1,?)
D)?descreasing on (-?,?)
E)descreasing on (1,1) increasing on (1,?)

Question

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 and has a minimum point. The vertex of this parabola can be found using the formula $x = -\frac{b}{2a}$, which gives $x = 1$. 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 $f ( x ) = 6 x ^ { 2 } - 12 x + 6$