ЯсноПонятно24

To solve this inequality, we need to find the critical points where the inequality changes sign.

First, let's find the critical points by setting the expression equal to zero and solving for x:

-x^6 + 3x^5 - 37x^4 + 8x^3 + 22x^2 + 72x - 88 = 0

We can use a numerical method or a computer algebra system to find the approximate solutions to this equation. The critical points are approximately x ≈ -1.45, x ≈ 0.78, and x ≈ 5.84.

Now, we can test the intervals defined by these critical points to determine where the inequality holds true.

Testing x < -1.45: Let's choose x = -2: -(-2)^6 + 3(-2)^5 - 37(-2)^4 + 8(-2)^3 + 22(-2)^2 + 72(-2) - 88 = -64 + 96 - 592 - 64 + 88 - 144 - 88 = -768 Since -768 < 0, the inequality holds true for x < -1.45.

Testing -1.45 < x < 0.78: Let's choose x = 0: -0^6 + 3(0)^5 - 37(0)^4 + 8(0)^3 + 22(0)^2 + 72(0) - 88 = -88 Since -88 < 0, the inequality does not hold true for -1.45 < x < 0.78.

Testing x > 0.78: Let's choose x = 1: -(1)^6 + 3(1)^5 - 37(1)^4 + 8(1)^3 + 22(1)^2 + 72(1) - 88 = -1 + 3 - 37 + 8 + 22 + 72 - 88 = -21 Since -21 < 0, the inequality holds true for x > 0.78.

Therefore, the solution to the inequality -x^6 + 3x^5 - 37x^4 + 8x^3 + 22x^2 + 72x - 88 ≥ 0 is x ≤ -1.45 or x ≥ 0.78.