Dick said:No. Express your curve as f(x,y)=C and use the gradient. That's what they told you to do.
-EquinoX- said:so the gradient will be the normal to the level curves??
-EquinoX- said:well the gradient I have is:
(-3y + 2x) i + (2y - 3x) j
is this true?
The gradient of a function is a vector that shows the rate of change of the function at a specific point. It is a measure of the steepness or slope of the function at that point.
To determine the gradient of a function, you need to find the partial derivatives of the function with respect to each variable. These partial derivatives are then used to calculate the gradient vector at a specific point.
The gradient provides important information about the behavior of a function. It can help determine the direction in which the function is increasing or decreasing, and can be used to find the maximum or minimum values of the function.
The gradient vector is always perpendicular to the level curves of a function. This means that the gradient shows the direction in which the function is changing the fastest, while the level curves show points where the function has the same value.
Yes, the gradient of a function can be negative. This happens when the function is decreasing in the direction of the gradient vector. However, the magnitude of the gradient is always positive as it represents the rate of change of the function.