Answer :
To find the value of the function [tex]\( f(x, y) = 3x^2 - 4y \)[/tex] at the point [tex]\((3, 2)\)[/tex], we follow these steps:
1. Substitute the values: Replace [tex]\( x \)[/tex] with 3 and [tex]\( y \)[/tex] with 2 in the function.
2. Calculate [tex]\( 3x^2 \)[/tex]:
[tex]\[
3 \times (3)^2 = 3 \times 9 = 27
\][/tex]
3. Calculate [tex]\( 4y \)[/tex]:
[tex]\[
4 \times 2 = 8
\][/tex]
4. Subtract the two results:
[tex]\[
27 - 8 = 19
\][/tex]
Thus, the value of [tex]\( f(3, 2) \)[/tex] is [tex]\(\boxed{19}\)[/tex].
1. Substitute the values: Replace [tex]\( x \)[/tex] with 3 and [tex]\( y \)[/tex] with 2 in the function.
2. Calculate [tex]\( 3x^2 \)[/tex]:
[tex]\[
3 \times (3)^2 = 3 \times 9 = 27
\][/tex]
3. Calculate [tex]\( 4y \)[/tex]:
[tex]\[
4 \times 2 = 8
\][/tex]
4. Subtract the two results:
[tex]\[
27 - 8 = 19
\][/tex]
Thus, the value of [tex]\( f(3, 2) \)[/tex] is [tex]\(\boxed{19}\)[/tex].
