Yes, the piecewise approach is what you should be using here.Estane said:Homework Statement
Show that ∇[itex]_{x}[/itex]|x-y|-3= -(x-y)|x-y|-3
x and y are vectors.
Homework Equations
The Attempt at a Solution
When dealing with just a straight up absolute value I know that a solution can be found by using a piece wise approach, but I don't think that's what I should be using here. The power is throwing me completely and I have no idea how to deal with it.
Thanks
The gradient of an absolute value raised to a power is the slope or rate of change of the function at any given point. It is calculated by taking the derivative of the function and evaluating it at the specific point.
To calculate the gradient of an absolute value raised to a power, you first take the derivative of the function. Then, you plug in the specific point at which you want to find the gradient. The resulting value is the gradient at that point.
The gradient of an absolute value raised to a power is significant because it tells us the direction and rate of change of the function at a specific point. It can be used to find the maximum and minimum values of the function, as well as to determine the concavity of the function.
The gradient of an absolute value raised to a power will change depending on the value of the power. For example, a higher power will result in a steeper slope, while a lower power will result in a flatter slope. The gradient will also change at different points along the function.
Yes, the gradient of an absolute value raised to a power can be negative. This means that the function is decreasing at that point. However, the absolute value itself will always be a positive value, so the negative gradient is simply indicating the direction of the change.