Identify the open intervals where the function $f ( x ) = 4 x ^ { 2 } - 5 x - 5$ is increasing or decreasing.
A)decreasing: $\left( - \infty , \frac { 5 } { 8 } \right)$ ; increasing: $\left( \frac { 5 } { 8 } , \infty \right)$
B)increasing: $\left( - \infty , \frac { 5 } { 8 } \right)$ ; decreasing: $\left( \frac { 5 } { 8 } , \infty \right)$
C)increasing on $( - \infty , \infty )$
D)decreasing on $( - \infty , \infty )$
E)none of the above

Question

Quizplus · Accepted Answer

To determine where the function is increasing or decreasing, we find the derivative of $f(x) = 4x^2 - 5x - 5$, which is $f'(x) = 8x - 5$. Setting $f'(x) = 0$ gives $x = \frac{5}{8}$. Since the coefficient of $x^2$ in $f(x)$ is positive, the function is concave up, meaning it decreases before $x = \frac{5}{8}$ and increases after.

Identify the Open Intervals Where the Function f(x)=4x2−5x−5f ( x ) = 4 x ^ { 2 } - 5 x - 5f(x)=4x2−5x−5

Identify the Open Intervals Where the Function $f ( x ) = 4 x ^ { 2 } - 5 x - 5$