Answer :
To find the value of [tex]\( f(6) \)[/tex] for the function [tex]\( f(x) = \frac{2}{3} x^2 + 8x \)[/tex], follow these steps:
1. Substitute [tex]\( x = 6 \)[/tex] into the function:
Start with the function [tex]\( f(x) = \frac{2}{3} x^2 + 8x \)[/tex] and substitute [tex]\( x = 6 \)[/tex] into the expression. This gives:
[tex]\[
f(6) = \frac{2}{3} \times 6^2 + 8 \times 6
\][/tex]
2. Calculate [tex]\( 6^2 \)[/tex]:
[tex]\( 6^2 \)[/tex] is [tex]\( 36 \)[/tex]. So, the expression becomes:
[tex]\[
f(6) = \frac{2}{3} \times 36 + 8 \times 6
\][/tex]
3. Multiply [tex]\(\frac{2}{3}\)[/tex] and [tex]\(36\)[/tex]:
[tex]\(\frac{2}{3} \times 36 = 24\)[/tex].
4. Calculate [tex]\( 8 \times 6 \)[/tex]:
[tex]\( 8 \times 6 = 48 \)[/tex].
5. Add the results:
Now, add the two numbers from steps 3 and 4:
[tex]\[
24 + 48 = 72
\][/tex]
Therefore, the value of [tex]\( f(6) \)[/tex] is 72. So the correct answer is option B.
1. Substitute [tex]\( x = 6 \)[/tex] into the function:
Start with the function [tex]\( f(x) = \frac{2}{3} x^2 + 8x \)[/tex] and substitute [tex]\( x = 6 \)[/tex] into the expression. This gives:
[tex]\[
f(6) = \frac{2}{3} \times 6^2 + 8 \times 6
\][/tex]
2. Calculate [tex]\( 6^2 \)[/tex]:
[tex]\( 6^2 \)[/tex] is [tex]\( 36 \)[/tex]. So, the expression becomes:
[tex]\[
f(6) = \frac{2}{3} \times 36 + 8 \times 6
\][/tex]
3. Multiply [tex]\(\frac{2}{3}\)[/tex] and [tex]\(36\)[/tex]:
[tex]\(\frac{2}{3} \times 36 = 24\)[/tex].
4. Calculate [tex]\( 8 \times 6 \)[/tex]:
[tex]\( 8 \times 6 = 48 \)[/tex].
5. Add the results:
Now, add the two numbers from steps 3 and 4:
[tex]\[
24 + 48 = 72
\][/tex]
Therefore, the value of [tex]\( f(6) \)[/tex] is 72. So the correct answer is option B.
