What you've done is almost fine but you have to be more clear and careful with mathematical expressions like:

When you read it like this, this doesn't make sense although you mean:

So we have two zero's and

To determine if you're dealing with a minimum or a maximum you can make a sign table (I guess you've done something like that):

You get a maximum and a minimum (review this)

To determine if there're points of inflection then you've to use the second derivative ...