Find all critical numbers for the function $f ( x ) = \left| x ^ { 2 } - 9 \right|$ .
A)0
B)-3
C)0, -3
D)No Critical Number
E)3
F)3, -3
G)0, 3, -3
H)None of the above

Question

Quizplus · Accepted Answer

The critical numbers occur where the derivative is zero or undefined. The function $f(x) = |x^2 - 9|$ has critical points where $x^2 - 9 = 0$ (i.e., $x = 3$ or $x = -3$) and where the derivative changes due to the absolute value, which is at $x = 0$.

Find All Critical Numbers for the Function f(x)=∣x2−9∣f ( x ) = \left| x ^ { 2 } - 9 \right|f(x)=​x2−9​

Find All Critical Numbers for the Function $f ( x ) = \left| x ^ { 2 } - 9 \right|$