You need to look for points to the left of which the gradient is positive and to the right of which the gradient is negative (or vice versa). This is all a stationary point on a quadratic graph is. Here, we don't have a quadratic graph, we have a graph which is linear for
x<0 and quadratic for
x≥0. The stationary point of the quadratic graph lies at
x=1, and so that is one local extremum. There is, however, another extremum, which can't be found by differentiating. When you draw the graph, you'll see that there's a spike that appears at
x=0, before which the gradient is negative and after which the gradient is positive.