In neural networks, activation functions introduce non-linearities, enabling the network to approximate complex functions. One of the desirable properties for an activation function is to be zero-centered. Being zero-centered helps in achieving faster convergence during training, as the weights can adjust in both positive and negative directions more efficiently. Addition- ally, zero-centered functions can help mitigate the vanishing gradient problem, ensuring that gradients during backpropagation don't diminish too quickly. Definition: A function g(x) is said to be zero-centered if, for every value x in its domain where g(x) is positive, there exists an equivalent negative value x such that: g(x) = g(x) In other words, the function is symmetric around the y-axis, producing positive outputs for positive inputs and negative outputs for negative inputs. Given the context and definition above, consider a zero-centered activation function g(x). Show that if its derivative g(x) exists, then g(0) = 0