Well, at the stationary points the gradient will equal zero. Essentially, find the points where the gradient is equal to zero, as that'll tell you where the stationary points are located.
Then, do find their nature, there are a few different ways. I was taught how to do it with a simple table, but it's been a while, and there are other ways I was shown at university. Your question says you must use differentiation but I never once encountered a question in any higher maths exam that said you must use differentiation to find the stationary points - I never did and was never taught to until after I sat the exam.