Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-$$f ( x ) = x ^ { 2 } - 10 x - 24$$
A) Increasing on $( - \infty , - 5 )$; decreasing on $( - 5 , \infty )$
B) Increasing on $( - \infty , 5 )$; decreasing on $( 5 , \infty )$
C) Increasing on $( 5 , \infty )$; decreasing on $( - \infty , 5 )$
D) Increasing on $( - 5 , \infty )$; decreasing on $( - \infty , - 5 )$

Question

Quizplus · Accepted Answer

To determine where the function is increasing or decreasing, we find the derivative of the function: $f'(x) = 2x - 10$. Setting the derivative equal to zero gives us the critical point: $2x - 10 = 0 \Rightarrow x = 5$. Since the coefficient of $x^2$ in the original function is positive, the function is concave up, meaning it decreases before $x = 5$ and increases after $x = 5$. Therefore, the function is increasing on $(5, \infty)$ and decreasing on $(- \infty, 5)$.

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