Which of the two functions below has the smallest minimum y-value?f(x) = (x - 13)4 - 2g(x) = 3x3 + 2A.The extreme minimum y-value for f(x) and g(x) is −∞−∞B.f(x)C.There is not enough information to determineD.g(x)SUBMITarrow_backPREVIOUS
Question
Which of the two functions below has the smallest minimum y-value?f(x) = (x - 13)4 - 2g(x) = 3x3 + 2A.The extreme minimum y-value for f(x) and g(x) is −∞−∞B.f(x)C.There is not enough information to determineD.g(x)SUBMITarrow_backPREVIOUS
Solution
The function f(x) = (x - 13)^4 - 2 has a minimum y-value at -2 when x = 13. This is because the term (x - 13)^4 is always positive or zero (for x = 13), so the smallest this function can be is -2.
The function g(x) = 3x^3 + 2 does not have a minimum y-value because it is a cubic function. As x approaches negative infinity, g(x) also approaches negative infinity.
Therefore, the function g(x) has the smallest minimum y-value, which is negative infinity. So, the answer is D. g(x).
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