$\operatorname { grad } f ( a , b )$ is perpendicular to the graph of $z = f ( x , y )$ at the point $( a , b , f ( a , b ) )$ .

Name: $\operatorname { grad } f ( a , b )$ is perpendicular to the graph of $z = f ( x , y )$ at the point $( a , b , f ( a , b ) )$ .
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Question

Quizplus · Accepted Answer

$\operatorname { grad } f ( a , b )$ is perpendicular to the level curve of $f$ at the point $( a , b )$, not to the graph of $z = f ( x , y )$. It points in the direction of the greatest rate of increase of $f$.

grad⁡f(a,b)\operatorname { grad } f ( a , b )gradf(a,b)

$\operatorname { grad } f ( a , b )$