When I went to pay at check out the turbo take price increased by $10 without cause

You are posting from Deluxe.  The fee for online Deluxe has been the same for months--$59.99 and the state is $44.99.  Are you seeing something different?

How can I see my TurboTax  fees?   

https://ttlc.intuit.com/questions/2565973-how-do-i-review-my-fees-in-turbotax-online

Or did you add a feature that you want to remove?

https://ttlc.intuit.com/questions/1899480-why-am-i-being-charged-for-turbotax-free-edition

There was a price increase back on March 1.  Did you start before then?  The price is determined at the time you pay or file.  You can pay early to lock in a lower price.

But $10 isn't much.  It could be the sales tax or just rounding.

Actually when the prices were first presented they listed the deluxe at 49.99 with the other prices. When I clicked that I did not want the premium it then took the premium fee off but also added $10 to the deluxe price making it 59 total.

I don't know what or when you saw Deluxe for 49.99 but Deluxe has been 59.99 since 3/1.   Before then it was 39.99.

Maybe you saw the Desktop CD/Download program price?  Desktop is totally different than the Online version.

They do raise the price later in the year from the early ads. I don't think they make that very clear. I remember getting a "lock in your fee" email one year but those emails are easy to miss and sometimes go straight to spam folder.