First, use
NewProb to clear your calculator for a
new problem.
Make sure
your calculator is in Auto mode.
Define
a function f to be some fairly simple
polynomial.
Define
f(x) = x^2+3x+4 will do the trick, but use your favorite coefficients.
Enter the formula for the slope of the line between the (abstract) points (x, f(x)) and (x+h, f(x+h)).
Enter ans(1)
on the command line (it's 2nd (-) ) and append |h=0
to the end.
You're recalculating
the slope with the two points so close together that they're really one
point.
If this
works, it should give the derivative of f at the point (x, f(x)),
which should be a general formula for f'(x).
If you want to save the steps you followed so you can use them again, read how to use the Text Editor.
If
you saved the procedure, you can use it to compute the derivative of any
rational function (quotient of two polynomials) with integer or fractional
coefficients. If your formula has a decimal point in it, the calculator
automatically changes to Approximate mode,
where you might not get a completely accurate answer.
For
more complicated functions, you will need to change the last command to
compute a limit instead of just substituting
a number for x. See below.
Repeat the procedure for f(x) = sin(x). What goes wrong at the end?
The calculator
automatically simplifies rational functions. (Though it's not always successful
when it works in Approximate mode.)
But the
sine function isn't an algebraic function.
Instead
of evaluating the slope of the line when h=0, take the limit of
the slope of the line as h approaches 0.
The command
you want is limit(ans(1),h,0).
Exercises