$\text { Find } \nabla f ( x , y ) \text { for function } f ( x , y ) = 8 - \frac { x } { 8 } - \frac { y } { 2 } \text {. }$
A) $\nabla f ( x , y ) = \frac { 1 } { 8 } \hat { \mathbf { i } } + \frac { 1 } { 2 } \hat { \mathbf { j } }$
B) $\nabla f ( x , y ) = \frac { 1 } { 8 } \hat { \mathbf { i } } - \frac { 1 } { 2 } \hat { \mathbf { j } }$
C) $\nabla f ( x , y ) = - 8 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }$
D) $\nabla f ( x , y ) = 8 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }$
E) $\nabla f ( x , y ) = - \frac { 1 } { 8 } \hat { \mathbf { i } } - \frac { 1 } { 2 } \hat { \mathbf { j } }$

Question

$\text { Find } \nabla f ( x , y ) \text { for function } f ( x , y ) = 8 - \frac { x } { 8 } - \frac { y } { 2 } \text {. }$ 
A) $\nabla f ( x , y ) = \frac { 1 } { 8 } \hat { \mathbf { i } } + \frac { 1 } { 2 } \hat { \mathbf { j } }$
B) $\nabla f ( x , y ) = \frac { 1 } { 8 } \hat { \mathbf { i } } - \frac { 1 } { 2 } \hat { \mathbf { j } }$
C) $\nabla f ( x , y ) = - 8 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }$
D) $\nabla f ( x , y ) = 8 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }$
E) $\nabla f ( x , y ) = - \frac { 1 } { 8 } \hat { \mathbf { i } } - \frac { 1 } { 2 } \hat { \mathbf { j } }$

Quizplus · Accepted Answer

The gradient $\nabla f(x, y)$ of the function $f(x, y) = 8 - \frac{x}{8} - \frac{y}{2}$ is found by taking the partial derivatives with respect to $x$ and $y$. The partial derivative with respect to $x$ is $-\frac{1}{8}$ and with respect to $y$ is $-\frac{1}{2}$, resulting in $\nabla f(x, y) = -\frac{1}{8}\hat{\mathbf{i}} - \frac{1}{2}\hat{\mathbf{j}}$.

Find ∇f(x,y) for function f(x,y)=8−x8−y2. \text { Find } \nabla f ( x , y ) \text { for function } f ( x , y ) = 8 - \frac { x } { 8 } - \frac { y } { 2 } \text {. } Find ∇f(x,y) for function f(x,y)=8−8x​−2y​.

$\text { Find } \nabla f ( x , y ) \text { for function } f ( x , y ) = 8 - \frac { x } { 8 } - \frac { y } { 2 } \text {. }$