$\text { Find the open interval(s) on which } f ( x ) = - 2 x ^ { 2 } + 12 x + 8 \text { is increasing or decreasing. }$
A) increasing on $( - \infty , 6 )$; decreasing on $( 6 , \infty )$
B) increasing on $( - \infty , 16 )$; decreasing on $( 16 , \infty )$
C) increasing on $( - \infty , 32 )$; decreasing on $( 32 , \infty )$
D) increasing on $( - \infty , 24 )$; decreasing on $( 24 , \infty )$
E) increasing on $( - \infty , 3 )$; decreasing on $( 3 , \infty )$

Question

$\text { Find the open interval(s) on which } f ( x ) = - 2 x ^ { 2 } + 12 x + 8 \text { is increasing or decreasing. }$ 
A) increasing on $( - \infty , 6 )$; decreasing on $( 6 , \infty )$
B) increasing on $( - \infty , 16 )$; decreasing on $( 16 , \infty )$
C) increasing on $( - \infty , 32 )$; decreasing on $( 32 , \infty )$
D) increasing on $( - \infty , 24 )$; decreasing on $( 24 , \infty )$
E) increasing on $( - \infty , 3 )$; decreasing on $( 3 , \infty )$

Quizplus · Accepted Answer

To determine where the function is increasing or decreasing, we find the derivative of $f(x) = -2x^2 + 12x + 8$, which is $f'(x) = -4x + 12$. Setting $f'(x) = 0$ gives $x = 3$. Since $f'(x) > 0$ for $x < 3$ and $f'(x) < 0$ for $x > 3$, the function is increasing on $(- \infty, 3)$ and decreasing on $(3, \infty)$.

Find the open interval(s) on which f(x)=−2x2+12x+8 is increasing or decreasing. \text { Find the open interval(s) on which } f ( x ) = - 2 x ^ { 2 } + 12 x + 8 \text { is increasing or decreasing. } Find the open interval(s) on which f(x)=−2x2+12x+8 is increasing or decreasing.

$\text { Find the open interval(s) on which } f ( x ) = - 2 x ^ { 2 } + 12 x + 8 \text { is increasing or decreasing. }$