Difference Quotient Calculation

[KeithB]

I was helping someone with some first year calculus, and they had to calculate the difference quotient:
https://en.wikipedia.org/wiki/Difference_quotient

Is there an easy way to do that symbolically in the CAS? Or is it purposely left out since this is something only first year calculus students would do, and then only for homework? 8^)

[froehlic]

One easy way might be to define a function e.g. F1(X) in function.
Change to CAS and type the difference quotient:

(F1(x+DELTA) + F1(x)) / DELTA

To see it a little bit better:

EXPAND(ANS)

Now you can get the derivative by applying the limes. You can double check it with the derivative (see screenshot).

[Albert Chan]

Slope is more accurate using central difference, CAS has it built-in.

CAS> nDeriv(f(x), x, h)

0.5*(f(h+x)-(f(-h+x)))/h

We can make it 1-sided.

CAS> nDeriv(f(x+h/2), x, h/2)

(-(f(x))+f(h+x))/h