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

Question

Quizplus · Accepted Answer

Taking the derivative of $y = \left( x ^ { 2 } - 9 \right) ^ { 2 }$, we get $y' = 4x(x^2-9)$. This is equal to zero at $x=0$ and $x=\pm 3$. Testing intervals around these zeros, we find that the function is increasing on the interval $(3,\infty)$. Therefore, the largest open interval where the function is increasing 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 $\quad y = \left( x ^ { 2 } - 9 \right) ^ { 2 }$