Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-$$f ( x ) = x ^ { 2 } - 5 x + 6$$
A) Increasing on $\left( \frac { 5 } { 2 } , \infty \right)$; decreasing on $\left( - \infty , \frac { 5 } { 2 } \right)$
B) Increasing on $\left( - \frac { 5 } { 2 } , \infty \right) ;$ decreasing on $\left( - \infty , - \frac { 5 } { 2 } \right)$
C) Increasing on $\left( - \infty , - \frac { 5 } { 2 } \right) ;$ decreasing on $\left( - \frac { 5 } { 2 } , \infty \right)$
D) Increasing on $\left( - \infty , \frac { 5 } { 2 } \right)$; decreasing on $\left( \frac { 5 } { 2 } , \infty \right)$

Question

Quizplus · Accepted Answer

To determine where the function is increasing or decreasing, we find its derivative: $f'(x) = 2x - 5$. Setting $f'(x) = 0$ gives $x = \frac{5}{2}$. This is the critical point where the function changes from decreasing to increasing. For $x < \frac{5}{2}$, $f'(x) < 0$, so the function is decreasing. For $x > \frac{5}{2}$, $f'(x) > 0$, so the function is increasing.

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