Consider the function f(x)=4(x−3^2/3. For this function there are two important intervals: (−�‡,A) and (A,�‡) where A is a critical number.

Find A

To find the critical number A for the function f(x)=4(x−3^2/3), we need to set the derivative of the function equal to zero and solve for x.

Step 1: Find the derivative of the function f(x).
f'(x) = 4 * (d/dx)[(x−3^2/3)]
= 4 * (1)
= 4

Step 2: Set the derivative equal to zero and solve for x.
4 = 0

Since 4 is a non-zero constant, it is never equal to zero. Therefore, there is no x value that makes the derivative equal to zero.

The function f(x)=4(x−3^2/3) is a linear function, and linear functions have a constant slope. Since the slope is always constant, there are no critical points.

Therefore, there is no critical number A for the given function. The two important intervals are (-∞, A] and [A, ∞).