Alright, let's evaluate the function [tex]\( f(x) = \frac{2}{3} x^2 + \frac{1}{2} x - 2 \)[/tex] at [tex]\( x = 6 \)[/tex].
1. Substitute [tex]\( x = 6 \)[/tex] into the function:
So, we have:
[tex]\[
f(6) = \frac{2}{3} (6)^2 + \frac{1}{2} (6) - 2
\][/tex]
2. Calculate [tex]\( (6)^2 \)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
3. Multiply [tex]\(\frac{2}{3}\)[/tex] by [tex]\( 36 \)[/tex]:
[tex]\[
\frac{2}{3} \times 36 = 24
\][/tex]
4. Multiply [tex]\(\frac{1}{2}\)[/tex] by [tex]\( 6 \)[/tex]:
[tex]\[
\frac{1}{2} \times 6 = 3
\][/tex]
5. Combine these results:
[tex]\[
f(6) = 24 + 3 - 2
\][/tex]
6. Perform the arithmetic:
[tex]\[
24 + 3 = 27
\][/tex]
[tex]\[
27 - 2 = 25
\][/tex]
So, the value of [tex]\( f(6) \)[/tex] is:
[tex]\[
\boxed{25}
\][/tex]
