I don't understand anything

I'll work through it first myself just to understand
But why differentiation btw?

At one point the gradient is 0
When u differentiate it, the y value of it will be 0 because original function's gradient is 0, making the x easy to find.
This is called a critical point
Usually, u would use the second derivative to find the nature of the turning point (being a max)
But here since I already know a vague shape of the graph, I know that this will be the local maximum, so I only need to use first derivative
now that i have the x value by subbing in y=0, i can plug it into the original function to get the y value of the point as well yayyyyy!!!!
THE END.