All you need to do, it's find the second derivative, and equal it to zero.
Solve for and you'll get the coordinates.
And as the second derivative is negative, the slope of the first derivative must be going down, which means the slope of the first derivative is decreasing, so the slope of the function is decreasing, so it is convexed down. (if positive, will go to zero, if negative will go to negative infinity.)
Now, there must be a point where they go from convexed up to convexed down and vice versa, and as you can see that it is the sign of the second derivative which determines this, then you can see that when the sign changes between positive and negative is when the graph of the function changes convex. So when the second derivative = zero, that is the point where its sign changes, so that is the point where the function changes convex, which is the point of inflection.