Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 5 x - 4$ . A)Decreasing for $x - \frac { 5 } { 2 }$ B)Decreasing for all x C)Increasing for all x D)Decreasing for $x - \frac { 5 } { 2 }$ and increasing for $x

Question

Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 5 x - 4$ . A)Decreasing for $x < - \frac { 5 } { 2 }$ and increasing for $x > - \frac { 5 } { 2 }$ B)Decreasing for all x C)Increasing for all x D)Decreasing for $x > - \frac { 5 } { 2 }$ and increasing for $x < - \frac { 5 } { 2 }$

Quizplus · Accepted Answer

To determine intervals of increase and decrease, we find the derivative of $f(x)$, which is $f'(x) = 2x + 5$. Setting $f'(x) = 0$ gives $x = -\frac{5}{2}$. The function decreases before $x = -\frac{5}{2}$ and increases after $x = -\frac{5}{2}$.

Find the Intervals of Increase and Decrease for the Function f(x)=x2+5x−4f ( x ) = x ^ { 2 } + 5 x - 4f(x)=x2+5x−4

Find the Intervals of Increase and Decrease for the Function $f ( x ) = x ^ { 2 } + 5 x - 4$