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Difference Quotient Calculation - KeithB - 09-07-2021 01:02 PM
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^)
RE: Difference Quotient Calculation - froehlic - 09-07-2021 02:27 PM
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).
RE: Difference Quotient Calculation - Albert Chan - 09-07-2021 02:33 PM
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