*{moderator edit - remove quiz question and solution}*

They must have covered how Gradient Descent works in the lectures. The gradient points in the direction of maximum increase of the function. So what we do to find a local minimum is multiply the gradient by -1 and move in the direction of maximum decrease of the value of the function. So if you start from that initial point and move in the opposite direction of the gradient, where will that take you? Towards the point P1, right?

i didâ€™nt get it

Sorry, just to make sure Iâ€™m clear on what you are saying: do you mean that the explanation I gave above didnâ€™t help you? Or are you saying that you missed it the first time, but now youâ€™re ok after reading what I said above?

yes , i didnt understand ur explanation, plus the content is not helping a lot

Take another look at the picture that you posted originally. Look at the position of the â€śinitial pointâ€ť on the curve. What is the derivative of the function at that point? It points up and to the right at about a 45 degree angle, right? So what direction will Gradient Descent take us if we take that derivative vector and multiply it by -\alpha where \alpha is the â€ślearning rateâ€ť? It will point down and to the left at about a negative 45 degree angle. So what Gradient Descent does is takes small steps in the direction of the negative of the gradient (derivative) and the size of the step is determined by the learning rate: in this case we will be taking small steps down and to the left, which takes us in the direction of the point P1.

As I mentioned before, I have not taken this course, but I know about Gradient Descent from DLS and I have a graduate degree in math and used to teach calculus to college students. So I am just basing my explanation off the picture and my understanding, but I donâ€™t actually know what words the MLS lectures say about all this. But my hope would be that what I just said would remind of you something that was said in the lectures. Then please go back and find that section of the lecture and watch it again and see if it helps.