Answer :

To find the value of the function [tex]\( f(x) = 3x^3 + 19x^2 + 11x + 21 \)[/tex] at [tex]\( x = -6 \)[/tex], follow these steps:

1. Substitute [tex]\(-6\)[/tex] into the function:

Replace every [tex]\( x \)[/tex] in the function with [tex]\(-6\)[/tex].
[tex]\[
f(-6) = 3(-6)^3 + 19(-6)^2 + 11(-6) + 21
\][/tex]

2. Calculate each term separately:

- The first term is [tex]\( 3(-6)^3 = 3 \times (-216) = -648 \)[/tex].
- The second term is [tex]\( 19(-6)^2 = 19 \times 36 = 684 \)[/tex].
- The third term is [tex]\( 11(-6) = -66 \)[/tex].
- The fourth term is simply [tex]\( 21 \)[/tex].

3. Combine all the terms:

Add the results from each step together:
[tex]\[
f(-6) = -648 + 684 - 66 + 21
\][/tex]

4. Simplify the expression:

- First, add [tex]\(-648\)[/tex] and [tex]\(684\)[/tex], which results in [tex]\(36\)[/tex].
- Then, add [tex]\(36\)[/tex] and [tex]\(-66\)[/tex], which results in [tex]\(-30\)[/tex].
- Finally, add [tex]\(-30\)[/tex] and [tex]\(21\)[/tex], which results in [tex]\(-9\)[/tex].

Therefore, the value of the function at [tex]\( x = -6 \)[/tex] is [tex]\(-9\)[/tex].

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Rewritten by : Barada