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Cocoleia
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Homework Statement
Homework Equations
The Attempt at a Solution
The answer is F. I don't how to get this. I know that it is perpendicular and must have a horizontal tangent. How do I come to this answer?[/B]
Let's look at one choice and see why it isn't an answer.Cocoleia said:Homework Statement
View attachment 110363
Homework Equations
The Attempt at a Solution
The answer is F. I don't how to get this. I know that it is perpendicular and must have a horizontal tangent. How do I come to this answer?[/B]
I understand, but why is f(x,y) = y- 2/xMark44 said:Let's look at one choice and see why it isn't an answer.
D. y = 2/x
Let f(x, y) = y - 2/x
Then ##\nabla f = <-2x^{-2}, 1>##, so ##\nabla f(1, 2) = <-2, 1> \ne \vec{j}##
I'm defining that way. With this definition, f(x, y) = 0 is equivalent to y = 2/x.Cocoleia said:I understand, but why is f(x,y) = y- 2/x
Can we always define it as being this way ?Mark44 said:I'm defining that way. With this definition, f(x, y) = 0 is equivalent to y = 2/x.
When you're talking about level curves, as this problem is, the equation y = 2/x represents the level curve f(x, y) = 0, with f(x, y) = y - 2/x.Cocoleia said:Can we always define it as being this way ?
A level curve is a curve on a three-dimensional graph that represents the set of points where a function has a constant value. This value is known as the level or contour value.
The gradient of a function is a vector that points in the direction of the steepest increase of the function at a given point. It is calculated by taking the partial derivatives of the function with respect to each independent variable.
To find the level curve through a given point, you must first calculate the gradient of the function at that point. Then, you can use the gradient vector to find the direction in which the level curve passes through the point. Finally, you can use this information to plot the level curve on the graph.
Finding the level curve through a point on the gradient allows us to visualize the behavior of a function in a specific direction. This can be helpful in understanding the overall shape of a function and identifying any critical points or extrema.
No, the level curve through a point on the gradient cannot intersect itself. This is because a level curve represents a set of points with the same value, and if it were to intersect itself, it would have two different values at the same point, which is not possible for a function.