1. partial derivatives

hi
can someone plz help me with this question

The point (3,1) lies on the level curve f(x,y)=10 of the function f(x,y) . The partial derivatives at this point are fx(3,1)=2 and fy(3,1)=-5. What is the slope of the tangent line to the level curve at the point (3,1) ?
kind regards

2. Originally Posted by lalji
hi
can someone plz help me with this question

The point (3,1) lies on the level curve f(x,y)=10 of the function f(x,y) . The partial derivatives at this point are fx(3,1)=2 and fy(3,1)=-5. What is the slope of the tangent line to the level curve at the point (3,1) ?
kind regards
$\nabla f(x,y)= 2\vec{i}- 5\vec{j}$ points perpendicular to the tangent to the level curves so the tangent vector is parallel to $5\vec{i}+ 2\vec{j}$. Can you find the slope from that?