Unable to update data into database using enity framework

//For Saving and updating if you are using linq to entities

using (CustomerEntities customerDataContext= new CustomerEntities())
{
    Customer customer = (from c in customerDataContext.Customers
             where c.Name == "customer name"
             selext c).First();

   if(customer !=null)
   {
     c.Name = "New Customer Name";
   }

    customerDataContext.Customers.SaveChanges();
}