Use the gradient to find a normal vector to the graph of the equation at the given point. $$2 x ^ { 2 } - y = 8 , \quad ( 6,64 )$$
A) $24 \hat { \mathbf { i } } + \hat { \mathbf { j } }$
B) $24 \hat { \mathbf { i } } - \hat { \mathbf { j } }$
C) $- 24 \hat { \mathbf { i } } - 64 \hat { \mathbf { j } }$
D) $- 24 \hat { \mathbf { i } } - \hat { \mathbf { j } }$
E) $24 \hat { \mathbf { i } } + 64 \hat { \mathbf { j } }$

Question

Quizplus · Accepted Answer

The gradient of the function $f(x, y) = 2x^2 - y - 8$ is $\nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right) = (4x, -1)$. At the point (6, 64), this becomes $24\hat{\mathbf{i}} - \hat{\mathbf{j}}$, which is a normal vector to the graph at that point.

Use the Gradient to Find a Normal Vector to the Graph