1. The problem is to analyze the function $f(x) = x^3 - 12x^2 + 36x$ and determine for which integer values of $x$ from 0 to 6 the function value is at least 5. 2. The function is given by: $$f(x) = x^3 - 12x^2 + 36x$$ 3. We want to check the condition: $$f(x) \geq 5$$ for $x = 0, 1, 2, 3, 4, 5, 6$. 4. Calculate $f(x)$ for each $x$: - $f(0) = 0^3 - 12\cdot0^2 + 36\cdot0 = 0$ - $f(1) = 1 - 12 + 36 = 25$ - $f(2) = 8 - 48 + 72 = 32$ - $f(3) = 27 - 108 + 108 = 27$ - $f(4) = 64 - 192 + 144 = 16$ - $f(5) = 125 - 300 + 180 = 5$ - $f(6) = 216 - 432 + 216 = 0$ 5. Check which values satisfy $f(x) \geq 5$: - $x=0$: $0 \not\geq 5$ (False) - $x=1$: $25 \geq 5$ (True) - $x=2$: $32 \geq 5$ (True) - $x=3$: $27 \geq 5$ (True) - $x=4$: $16 \geq 5$ (True) - $x=5$: $5 \geq 5$ (True) - $x=6$: $0 \not\geq 5$ (False) 6. Therefore, the list representing these conditions for $x=0$ to $6$ is: $$[0, 1, 1, 1, 1, 1, 0]$$ This matches the output of the given code. Final answer: $$[0, 1, 1, 1, 1, 1, 0]$$