Given the function f, of, x, equals, x, to the power 4 , minus, 18, x, squared, comma*f*(*x*)=*x*4−18*x*2, determine all intervals on which f*f* is both decreasing and concave down. Answer only.

The function \( f(x) = x^4 - 18x^2 \) is decreasing and concave down on the interval:

\[ (-\infty, -3) \cup (0, 3) \]

Given the function f(x) = x^4 - 18x^2, determine all intervals on which f is both decreasing and concave down.

Explore how to determine the intervals where the function f(x) = x^4 - 18x^2 is both decreasing and concave down. This problem involves calculus concepts such as derivatives, concavity, and the first and second derivative tests. Ideal for students in advanced high school calculus courses.

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