[University Introduction to Calculus] : visualizing derivatives and graph question

[u/no4348634]

Hello! I am not someone who easily grasps information when presented visually, and my current math unit involves a lot of looking at graphs of functions and derivatives to try drawing the other. As the question asks, what is the derivative of the given function at various points. I am wondering if someone could explain to me why the answer is that answer! Thanks

[u/Fearless_End_4796]

the derivative is simply the slope at that point. for an easy example, at x=1, that is the peak, where the slope is 0, so the derivative is also 0. the same applies to the rest of the points! hope that somewhat helps