Determine where the function is increasing and where it is decreasing.
-$$g ( x ) = 6 x ^ { 2 } + 120 x + 564$$
A) increasing on $( - \infty , - 10 )$
decreasing on $( - 10 , \infty )$

B) decreasing on $( - \infty , 10 )$
increasing on $( 10 , \infty )$

C) decreasing on $( - \infty , - 10 )$
increasing on $( - 10 , \infty )$

D) increasing on $( - \infty , - 60 )$
decreasing on $( - 60 , \infty )$

Question

Determine where the function is increasing and where it is decreasing.
-$$g ( x ) = 6 x ^ { 2 } + 120 x + 564$$
A) increasing on $( - \infty , - 10 )$
decreasing on $( - 10 , \infty )$

B) decreasing on $( - \infty , 10 )$ 
 increasing on $( 10 , \infty )$

C) decreasing on $( - \infty , - 10 )$
 increasing on $( - 10 , \infty )$

D) increasing on $( - \infty , - 60 )$
decreasing on $( - 60 , \infty )$

Quizplus · Accepted Answer

The function $g(x) = 6x^2 + 120x + 564$ is a quadratic function with a positive leading coefficient (6), meaning it opens upwards and has a minimum point. The vertex of a parabola given by $ax^2 + bx + c$ is at $(-b/2a, c)$. Here, $a = 6$ and $b = 120$, so the x-coordinate of the vertex is $-120/(2*6) = -10$. This means the function is decreasing before $x = -10$ and increasing after $x = -10$.

Determine Where the Function Is Increasing and Where It Is g(x)=6x2+120x+564g ( x ) = 6 x ^ { 2 } + 120 x + 564g(x)=6x2+120x+564

Determine Where the Function Is Increasing and Where It Is $g ( x ) = 6 x ^ { 2 } + 120 x + 564$