Update my 3.5 year old RCA 10in tablet

There may not be one, did you check in the settings if there is one available? Low end tablets don't often keep up with updates, they just churn them out and go on to the next model.
 
Unfortunately, this isn't a real solution. I spoke over a year ago with RCA's VP-Marketing about firmware and Android software updates. He informed me that at RCA's sub-$100 price point, updates were economically unfeasible.

My resolution to this problem was to sell RCA's crappy device and buy a real tablet (Samsung, LG, etc.) that gets regular updates.

Just goes to show that you get what you pay for. "The bitterness of poor quality is remembered long after the sweetness of low price is forgotten." How disappointing!