High School

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Consider the function [tex] f(x)=12x^5+60x^4-240x^3+1 [/tex]. For this function, there are four important intervals: [tex] (-\infty, A], [A, B], [B, C], [/tex] and [tex] [C, \infty) [/tex] where [tex] A, B, [/tex] and [tex] C [/tex] are constants that need to be determined.

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Answer :

Final answer:

The subject of this question is Mathematics. The grade level for this question is High School.

Explanation:

The subject of this question is Mathematics. The grade level for this question is High School.

To find the four important intervals for the given function, we need to determine the values of A, B, and C.

First, let's find the critical points of the function by taking the derivative and setting it equal to zero. The critical points are the values of x where the derivative is undefined or equal to zero.

Next, we use the critical points to divide the number line into the four intervals: (-∞, A], [A, B], [B, C], and [C, ∞).

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