obtain deriative of the function (dy/dx), then find the value(s)
of x when dy/dx = 0.
turning points can be a maximum (d²y/dx² < 0 when dy/dx = 0), a
minimum (d²y/dx² > 0) or a point of inflexion (d²y/dx² =
0).
for polynomials of degree 3 (ax³+bx²+cx+d or cubic equation), you
should have either:
for b² > 3ac, 2 turning points (1 max, 1 min)
for b² = 3ac, a single point of inflexion
for b² < 3ac, no turning points (dy/dx = 0 will have no real
solutions).