Final answer:
To find the tangent line to the level curve g(x,y)=31 at a given point, we need to find the slope of the tangent line at that point. The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point.
Step-by-step explanation:
To find the tangent line to the level curve g(x,y)=31 at a given point, we need to find the slope of the tangent line at that point. The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point.
Step-by-step solution:
- Determine the point on the curve where you want to find the tangent line.
- Calculate the slope of the tangent line at that point by finding the derivative of the curve with respect to the variable in question.
- Use the point-slope form of a line to write the equation of the tangent line.