Compute the gradient of the function at the given point.
-f(x, y) = 3x - 10y, (3, -4)
A)${\nabla} f = - 9 i - 40 j$
B) ${\nabla} f = 3 \mathbf { i } - 10 \mathbf { j }$
C)${\nabla} f = - 9 \mathrm { i } + 40 \mathrm { j }$
D) ${\nabla} f = - 3 \mathbf { i } - 4 \mathbf { j }$

Question

Compute the gradient of the function at the given point.
-f(x, y) = 3x - 10y, (3, -4) 
A)${\nabla} f = - 9 i - 40 j$
B) ${\nabla} f   = 3 \mathbf { i } - 10 \mathbf { j }$
C)${\nabla} f   = - 9 \mathrm { i } + 40 \mathrm { j }$
D) ${\nabla} f  = - 3 \mathbf { i } - 4 \mathbf { j }$

Quizplus · Accepted Answer

To compute the gradient of the function, we need to find the partial derivative of f with respect to x and y.

$$\frac{\partial f}{\partial x} = 3$$

$$\frac{\partial f}{\partial y} = -10$$

Therefore, the gradient of f is given by:

$${
abla} f = \frac{\partial f}{\partial x} \mathbf { i }+ \frac{\partial f}{\partial y} \mathbf { j } = 3 \mathbf { i } - 10 \mathbf { j }$$

At the point (3, -4), the gradient of f is:

$${
abla} f(3,-4) = 3 \mathbf { i } - 10 \mathbf { j }$$

Therefore, the best choice is B.

Compute the Gradient of the Function at the Given Point ∇f=−9i−40j{\nabla} f = - 9 i - 40 j∇f=−9i−40j

Compute the Gradient of the Function at the Given Point ${\nabla} f = - 9 i - 40 j$