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

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

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

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

Question

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

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

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

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

Quizplus · Accepted Answer

To determine where the function is increasing or decreasing, we find the derivative of the function $f(x) = -x^2 + 2x$. The derivative is $f'(x) = -2x + 2$. Setting $f'(x) = 0$ gives $x = 1$. The function is increasing when $f'(x) > 0$ and decreasing when $f'(x) < 0$. For $x < 1$, $f'(x) > 0$, so the function is increasing on $(- \infty, 1)$. For $x > 1$, $f'(x) < 0$, so the function is decreasing on $(1, \infty)$.

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

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