Consider the function y = (x + 4)^2 and assume the learning rate is 0.01. What is local minima of the function when x is initialized to 3? What is x after the first iteration using gradient descent?1 point0, 3.020, 4.08-4, 2.864, 3.8
Question
Consider the function y = (x + 4)^2 and assume the learning rate is 0.01. What is local minima of the function when x is initialized to 3? What is x after the first iteration using gradient descent?1 point0, 3.020, 4.08-4, 2.864, 3.8
Solution
The function y = (x + 4)^2 is a parabolic function, and its minimum value is achieved when x = -4. This is the local minimum of the function.
The gradient (or derivative) of the function y = (x + 4)^2 is dy/dx = 2*(x + 4).
If we initialize x to 3, the gradient at this point is 2*(3 + 4) = 14.
In gradient descent, we update x by subtracting the gradient times the learning rate from the current x. So, after the first iteration, the new x is:
x_new = x_old - learning_rate * gradient = 3 - 0.01 * 14 = 3 - 0.14 = 2.86
So, the local minimum of the function is -4, and x after the first iteration using gradient descent is 2.86.
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