Tom Miller wrote:

In the last 35 years I have used
calculus about once( to find a minimum point).

Not exactly important for the poster's question, but I actually find I
use calculus a lot, both in work and even in everyday life.

I don't mean I do integrals on cocktail napkins - that's not really the
point. What's important is the ways of seeing and addressing the world
that result from an understanding of calc. These can be very useful
hints for solving problems, even if 99% of the calc you do is more or
less "by eye". Real world calc problems tend to either be very simple,
not require a precise answer, or be messy enough that you just get a
numerical solution from the computer.

But back for a minute to doing calc by eye. A good graphical
visualization of what is going on is so much more usefull than being
able to use black magic on algebra, which is what the non-graphical
part amounts to. If we could teach graphical calc in mid-high school,
some of those ideas might actually get through. Instead we hit the
kids with 2nd and 3rd year algebra exercises which exist chiefly to set
up for the formal explanation of the calculus - a class most of them
won't take. We make them do 90% of the work of calc, but only show the
handful that survive that the dirty little tricks you can use to kill
off the inconvenient algebraic terms and be left with something that
simplifies down to a rewarding answer.