Curious about this answer, I use AI to help me understand a lot of what happens with questions like these, but as its not my expertise, I am always suspect of the answers i get. So I sent your question to Phind:
A good example of a function that is difficult to optimize by setting its first derivative to zero, but can be easily optimized using gradient descent, is the function f(x) = x*ln(x) - sqrt(x)
The derivative of this function is f’(x) = ln(x) + 1 - 1/(2*sqrt(x)). Setting this equal to zero does not yield a solution that can be expressed in terms of elementary functions. However, we can easily apply the gradient descent method to find a numerical solution.
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it also generated a bunch of example code in Python. Curious as to the validity of the response.
Curious about this answer, I use AI to help me understand a lot of what happens with questions like these, but as its not my expertise, I am always suspect of the answers i get. So I sent your question to Phind:
A good example of a function that is difficult to optimize by setting its first derivative to zero, but can be easily optimized using gradient descent, is the function f(x) = x*ln(x) - sqrt(x)
The derivative of this function is f’(x) = ln(x) + 1 - 1/(2*sqrt(x)). Setting this equal to zero does not yield a solution that can be expressed in terms of elementary functions. However, we can easily apply the gradient descent method to find a numerical solution.
*********************************
it also generated a bunch of example code in Python. Curious as to the validity of the response.