f(x) = any graphable function
f'(x) = the derivative of that function.

stationary points occur when f'(x) = 0

to establish whether or not it is a maximum turning point (looks like a hill), minimum turning point (looks like the letter 'U') or a point of inflexion/inflection (looks like a letter 'S', kinda), use a table of sign to establish the sign of f'(x) just before and just after the point where f'(x) = 0

EXAMPLE

f(x) = x^2 + 6

=> f'(x) = 2x
when 2x=0, x=0

there is a s.p at x = 0

at x=0, f(x)=6

the s.p. for this curve is the point (0,6)

Is it a maximum, minimum or p.o.i?

f'(x) = 2x
when x=-0.000001, f'(x) is -ve (sloping downwards)
when x = +0.000001, f'(x) is +ve (sloping upwards)

=> there is a MINIMUM S.P. at the point (0,6)

Same, good luck fellow computers