That is a reasonable approach but the number you get will include points where the slope is increasing, then the slope becomes 0, then increases again, if I remember correctly these are called inflection points, for example x^{3 }does this. Also you might have some non-unique turning points, for example x^{4}has turning points when 4x^{3}=0 and factorizing that shows that the 3 tuning points are all at x=0.