Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-$$f ( x ) = x ^ { 2 } - 8 x + 7$$
A) Increasing on $( 4 , \infty )$; decreasing on $( - \infty , 4 )$
B) Increasing on $( - 4 , \infty )$; decreasing on $( - \infty , - 4 )$
C) Increasing on $( - \infty , - 4 )$; decreasing on $( - 4 , \infty )$
D) Increasing on $( - \infty , 4 )$; decreasing on $( 4 , \infty )$

Question

Quizplus · Accepted Answer

To determine where the function is increasing or decreasing, we find the derivative of the function, $f'(x) = 2x - 8$. Setting $f'(x) = 0$ gives $x = 4$. This is the critical point where the function changes from increasing to decreasing or vice versa. For $x < 4$, $f'(x)$ is negative, indicating the function is decreasing. For $x > 4$, $f'(x)$ is positive, indicating the function is increasing. Therefore, the function is increasing on $(4, \infty)$ and decreasing on $(- \infty, 4)$.

Find the Intervals on Which the Function Is Increasing and the Intervals