Calculate $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) }$ , and $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) }$ when defined. $f ( x , y ) = 960 - 13 x + 6 y + 7 x y$
A) $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) } = - 22$ , $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) } = - 34$
B) $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) } = 110$ , $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) } = 136$
C) $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) } = 28$ , $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) } = 5$
D) $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) } = 22$ , $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) } = 34$
E) $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) } = 34$ , $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) } = 22$

Question

Calculate $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) }$ , and $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) }$ when defined.   $f ( x , y ) = 960 - 13 x + 6 y + 7 x y$  
A) $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) } = - 22$ , $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) } = - 34$
B) $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) } = 110$ , $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) } = 136$
C) $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) } = 28$ , $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) } = 5$
D) $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) } = 22$ , $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) } = 34$
E) $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) } = 34$ , $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) } = 22$

Quizplus · Accepted Answer

To find $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) }$, differentiate $f(x, y) = 960 - 13x + 6y + 7xy$ with respect to $x$, treating $y$ as a constant. This gives $\frac { \partial f } { \partial x } = -13 + 7y$. Substituting $x = 4, y = 5$ gives $\frac { \partial f } { \partial x } = -13 + 7(5) = -13 + 35 = 22$.To find $\left. \frac { \partial f } { \partial y } \right| _ { ( 4,5 ) }$, differentiate $f(x, y)$ with respect to $y$, treating $x$ as a constant. This gives $\frac { \partial f } { \partial y } = 6 + 7x$. Substituting $x = 4, y = 5$ gives $\frac { \partial f } { \partial y } = 6 + 7(4) = 6 + 28 = 34$.

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Calculate $\left. \frac { \partial f } { \partial x } \right| _ { ( 4,5 ) }$