Question

How can you tell the function have a maximum value than a minimum value ?

Answer 1

Find y' and set it to 0. Find x's to y'=0 to. Discuss the situation of each x and the intervals between them.
http://tutorial.math.lamar.edu/Classes/CalcI/DerivativeInterp.aspx
Be aware, u may need to discuss if the function is continuous or not, and if the x is a singularity or not.

Answer 2

you can also tell the difference by looking at 2nd derivative:

if y'' > 0 , then its a min
if y'' < 0 , then its a max