Determine where the function is increasing and where it is decreasing.
-$$f ( x ) = - 4 x ^ { 2 } - 2 x - 11$$
A) increasing on $\left( - \infty , - \frac { 1 } { 4 } \right)$
decreasing on $\left( - \frac { 1 } { 4 } , \infty \right)$
B) increasing on $\left( - \infty , \frac { 1 } { 4 } \right)$
decreasing on $\left( \frac { 1 } { 4 } , \infty \right)$

C) decreasing on $\left( - \infty , - \frac { 1 } { 4 } \right)$
increasing on $\left( - \frac { 1 } { 4 } , \infty \right)$

D) increasing on $\left( - \infty , - \frac { 43 } { 4 } \right)$
decreasing on $\left( - \frac { 43 } { 4 } , \infty \right)$

Question

Determine where the function is increasing and where it is decreasing.
-$$f ( x ) = - 4 x ^ { 2 } - 2 x - 11$$
A) increasing on $\left( - \infty , - \frac { 1 } { 4 } \right)$
 decreasing on $\left( - \frac { 1 } { 4 } , \infty \right)$
B) increasing on $\left( - \infty , \frac { 1 } { 4 } \right)$
decreasing on $\left( \frac { 1 } { 4 } , \infty \right)$

C) decreasing on $\left( - \infty , - \frac { 1 } { 4 } \right)$
increasing on $\left( - \frac { 1 } { 4 } , \infty \right)$

D) increasing on $\left( - \infty , - \frac { 43 } { 4 } \right)$ 
decreasing on $\left( - \frac { 43 } { 4 } , \infty \right)$

Quizplus · Accepted Answer

To determine where the function is increasing or decreasing, we find the derivative of the function and analyze its sign. The derivative of $f(x) = -4x^2 - 2x - 11$ is $f'(x) = -8x - 2$. Setting $f'(x) = 0$ gives $x = -\frac{1}{4}$. Since the coefficient of $x^2$ in the original function is negative, the function opens downwards, meaning it increases to the left of $-\frac{1}{4}$ and decreases to the right.

Determine Where the Function Is Increasing and Where It Is f(x)=−4x2−2x−11f ( x ) = - 4 x ^ { 2 } - 2 x - 11f(x)=−4x2−2x−11

Determine Where the Function Is Increasing and Where It Is $f ( x ) = - 4 x ^ { 2 } - 2 x - 11$