Answer :
Final Answer:
The least non-negative integral upper bound of the function f(x) is 7.
Explanation:
To find the least non-negative integral upper bound of the given function f(x) = 6x⁴ + 23x³ + 15x² - 23x - 21, we need to identify the largest value of x for which the function remains non-negative.
First, we can observe that for large positive values of x, the term 6x⁴ dominates, making the function positive. However, we need to ensure that it stays positive for x ≥ 0.
To find this boundary, we set the function equal to zero and solve for x:
6x⁴ + 23x³ + 15x² - 23x - 21 = 0
By analyzing this equation, we can see that the least non-negative integral upper bound is x = 7. At x = 7, the function changes sign from negative to positive, making 7 the minimum non-negative integral upper bound.
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