Determine where the function is increasing and where it is decreasing.
-$$f ( x ) = - x ^ { 2 } + 2 x + 8$$
A) increasing on $( - \infty , 1 )$
decreasing on $( 1 , \infty )$

B) increasing on $( 9 , \infty )$
decreasing on $( - \infty , 9 )$

C) increasing on $( 1 , \infty )$
decreasing on $( - \infty , 1 )$

D) increasing on $( - \infty , 9 )$
decreasing on $( 9 , \infty )$

Question

Determine where the function is increasing and where it is decreasing.
-$$f ( x ) = - x ^ { 2 } + 2 x + 8$$
A) increasing on $( - \infty , 1 )$
decreasing on $( 1 , \infty )$

B) increasing on $( 9 , \infty )$  
decreasing on $( - \infty , 9 )$

C) increasing on $( 1 , \infty )$
 decreasing on $( - \infty , 1 )$

D) increasing on $( - \infty , 9 )$
decreasing on $( 9 , \infty )$

Quizplus · Accepted Answer

To determine where the function is increasing or decreasing, we find the derivative of the function $f'(x) = -2x + 2$. Setting the derivative equal to zero gives the critical point $x = 1$. Since the coefficient of $x^2$ is negative, the function opens downwards, making it increase before the critical point and decrease after. Therefore, it is increasing on $(- \infty , 1)$ and decreasing on $(1 , \infty)$.

Determine Where the Function Is Increasing and Where It Is f(x)=−x2+2x+8f ( x ) = - x ^ { 2 } + 2 x + 8f(x)=−x2+2x+8

Determine Where the Function Is Increasing and Where It Is $f ( x ) = - x ^ { 2 } + 2 x + 8$