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

To determine where the function is increasing or decreasing, we find the derivative of the function $g(x) = 6x^2 + 120x + 564$. The derivative is $g'(x) = 12x + 120$. Setting $g'(x) = 0$ gives $12x + 120 = 0$, which solves to $x = -10$. Since the coefficient of $x^2$ in the original function is positive, the function opens upwards, making it 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 $g ( x ) = 6 x ^ { 2 } + 120 x + 564$