Find the largest open interval where the function is changing as requested.
-Increasing $\quad y = \left( x ^ { 2 } - 9 \right) ^ { 2 }$
A) $( - 3,3 )$
B) $( 3 , \infty )$
C) $( - \infty , 0 )$
D) $( - 3,0 )$

Question

Quizplus · Accepted Answer

To find where the function is increasing, we need to find the intervals where the derivative is positive. 
\begin{align*}
y &= \left( x ^ { 2 } - 9 ight) ^ { 2 }\
y' &= 2(x^2-9)(2x)\
&= 4x(x^2-9)
\end{align*}
The derivative is positive when $4x(x^2-9)>0$. This occurs when either $x>3$ or $x<-3$. Therefore, the function is increasing on the interval $(-\infty, -3) \cup (3, \infty)$. The largest open interval is $(3, \infty)$.

Find the Largest Open Interval Where the Function Is Changing y=(x2−9)2\quad y = \left( x ^ { 2 } - 9 \right) ^ { 2 }y=(x2−9)2

Find the Largest Open Interval Where the Function Is Changing $\quad y = \left( x ^ { 2 } - 9 \right) ^ { 2 }$