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Find the x-values of all points where the f(x)=-8/3x³-25/2x²-3x+15

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Final answer:

To find the x-values for points on the function f(x)=-8/3x³-25/2x²-3x+15, the function should be set to zero and solved for x using numerical methods or factoring, as it is a cubic function that does not factor easily.

Step-by-step explanation:

The student is asking to find the x-values at which the function f(x) = -8/3x³ - 25/2x² - 3x + 15 has points.

To find these values, we need to set the function equal to zero and solve for x, which may require using numerical methods or factoring if possible since the equation is a cubic function.

The equation does not factor nicely, so numerical methods such as synthetic division, the Rational Root Theorem, or a graphing calculator might be necessary to find approximate x-intercepts.

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