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Elihu5991 said:
You mean y', not y.Elihu5991 said:
Optimisation using calculus is a mathematical method used to find the maximum or minimum values of a function. It involves using derivatives to determine the slope of a curve and identify points where the slope is equal to zero, which correspond to maximum or minimum values.
Optimisation using calculus is important because it allows us to solve real-world problems that involve finding the best possible outcome. This can be applied in various fields such as economics, engineering, and science to make informed decisions and improve processes.
The key steps in optimisation using calculus include identifying the objective function, finding the first and second derivatives of the function, setting the first derivative equal to zero to find critical points, evaluating the second derivative at these points to determine whether they are maximum or minimum values, and finally, checking the endpoints of the given interval to ensure the global maximum or minimum is found.
Yes, optimisation using calculus can be applied to multivariable functions. In this case, the partial derivatives of the function are used to find critical points, and the Hessian matrix is used to determine whether these points are maximum or minimum values.
One limitation of optimisation using calculus is that it requires the function to be continuous and differentiable in the given interval. This means that it may not be applicable to some real-world problems that involve non-differentiable functions or discontinuities. Additionally, it may not always provide the most optimal solution, as there could be multiple critical points or the global maximum/minimum may not exist.
