The numeric value of the function when x = -2/3 is given by:
[tex]f\left(-\frac{2}{3}\right) = \frac{8}{27}[/tex]
How to find the numeric value of a function?
The numeric value of a function is found replacing each instance of x by the value that we want to find.
In this problem, the expression is given by:
[tex]f(x) = -\frac{3}{2}x^3 - \frac{1}{3}x^2[/tex]
For this problem, we want to find the numeric value of the function when x = -2/3, hence each of the two instances of x have to be replaced by -2/3, so:
[tex]f(x) = -\frac{3}{2}x^3 - \frac{1}{3}x^2[/tex]
[tex]f\left(-\frac{2}{3}\right) = -\frac{3}{2}(-\frac{2}{3}\right)^3 - \frac{1}{3}(-\frac{2}{3}\right)^2[/tex]
[tex]f\left(-\frac{2}{3}\right) = \frac{3 \times 2^3}{2 \times 3^3} - \frac{2^2}{3^3}[/tex]
[tex]f\left(-\frac{2}{3}\right) = \frac{12}{3^3} - \frac{4}{3^3}[/tex]
[tex]f\left(-\frac{2}{3}\right) = \frac{8}{27}[/tex]
More can be learned about the numeric values of a function at https://brainly.com/question/14556096
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