- #1
daniel69
- 10
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for the equation... y = x^3 - 2x^2 -5x +2
is its local minima at (2.120,-8.061)
Thanks
is its local minima at (2.120,-8.061)
Thanks
JonF said:i just look at the hessian to figure out if it's a min or not
Since this is a function of a single variable, its "Hessian" is just its second derivative. However, that would be assuming that the x value given really does give either a maximum or a minimum- which, I think, was part of the question.JonF said:i just look at the hessian to figure out if it's a min or not
A local minimum is a point on a graph where the function reaches its lowest value within a small interval of the point. It is lower than all the nearby points, but not necessarily the absolute lowest point on the entire graph.
To find the local minima of a function, you need to take its derivative and set it equal to zero. Then, solve for the x-values that make the derivative equal to zero. These x-values are the coordinates of the local minima on the graph.
The equation for finding local minima is f'(x) = 0, where f'(x) is the derivative of the function. Once you solve for the x-values that make the derivative equal to zero, you can plug them back into the original function to get the corresponding y-values.
Yes, a function can have multiple local minima. This can happen when the function has multiple "hills and valleys" or when the function is flat in certain areas.
To determine if a point is a local minimum on a graph, you can look at the slope of the function at that point. If the slope is positive on either side of the point, it is a local minimum. Additionally, you can also take the second derivative of the function at that point. If the second derivative is positive, the point is a local minimum.