Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 9 x - 5$ A) Decreasing for $x - \frac { 9 } { 2 }$ B) Increasing for all x C) Decreasing for $x - \frac { 9 } { 2 }$ and increasing for $x

Question

Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 9 x - 5$ A) Decreasing for $x < - \frac { 9 } { 2 }$ and increasing for $x > - \frac { 9 } { 2 }$ B) Increasing for all x C) Decreasing for $x > - \frac { 9 } { 2 }$ and increasing for $x < - \frac { 9 } { 2 }$ D) Decreasing for all x

Quizplus · Accepted Answer

To determine intervals of increase and decrease, we find the derivative of $f(x)$, which is $f'(x) = 2x + 9$. Setting $f'(x) = 0$ gives $x = -\frac{9}{2}$. The sign of $f'(x)$ changes from negative to positive at $x = -\frac{9}{2}$, indicating $f(x)$ is decreasing for $x < -\frac{9}{2}$ and increasing for $x > -\frac{9}{2}$.

Find the Intervals of Increase and Decrease for the Function f(x)=x2+9x−5f ( x ) = x ^ { 2 } + 9 x - 5f(x)=x2+9x−5

Find the Intervals of Increase and Decrease for the Function $f ( x ) = x ^ { 2 } + 9 x - 5$