Working principle for finding maxima and minima

1.Let y=f(x) be a given function

calculate dy/dx=f ' (x) and equate it to zero...sove for x..say x=a,b

2.calculate d²y/dx²=f ' '(x)

3.for x=a...f ' ' (a)<0,then f(x)max at x=a and max value is f(a)

similarly for minimum...