I think you have the basic idea down, but have made a mistake in the "simple" computation. At (-1, 1) the gradient of f is the zero vector. Both components of the gradient have factors of 3(y - x2)2. When x = -1, y = 1, this factor is 3(1 - (-1)2)2, or 0.Geometrick said:Homework Statement
You are at P(-1,1) on the surface z = (y-x^2)^3. What direction should you move from P so that your height remains the same?
Homework Equations
The Attempt at a Solution
So I basically do not want my height z to change. In this case, I will take a vector perpendicular to grad f(p), a simple computation shows that grad f(p) will be in the direction of <1,2>, so I take my direction v to be v = <-2, 1>.
I'm just wondering if this is correct?
The Gradient Problem Move From P(-1,1) refers to a mathematical concept where the slope or gradient of a function at a given point (P) is undefined or infinite. This can happen when there is a sharp or sudden change in the function at that point.
The Gradient Problem Move From P(-1,1) is important because it can affect the accuracy of mathematical models and calculations. It can also lead to difficulties in interpreting and analyzing data.
The Gradient Problem Move From P(-1,1) can be caused by discontinuities, sharp turns, or points of inflection in a function. It can also occur when there are undefined or infinite values in the function.
The Gradient Problem Move From P(-1,1) can be solved by carefully analyzing the function and identifying the source of the problem. In some cases, it may be possible to smooth out the function or approximate the gradient at the problematic point.
The Gradient Problem Move From P(-1,1) can occur in various fields such as physics, economics, and engineering. It is important to address this problem in order to accurately model and predict real-world phenomena, such as the behavior of stocks, the trajectory of a projectile, or the flow of fluids.