The difference quotient is
First find f(x+h) by substituting (x+h)
for each x in
f(x) = 2x² - 5x + 3
f(x+h) = 2(x+h)² - 5(x+h) + 3
f(x+h) = 2(x+h)(x+h) - 5(x+h) + 3
f(x+h) = 2(x²+hx+hx+h²) - 5x - 5h + 3
f(x+h) = 2(x²+2hx+h²) - 5x - 5h + 3
f(x+h) = 2x² + 4hx + 2h² - 5x - 5h + 3
No we substitute that for the f(x+h) in
and we have:
and we substitute (2x² - 5x + 3) for f(x), making sure
that we place it inside parentheses, so as not to get
any signs wrong since it is preceded by a - sign:
Now we remove the parentheses by changing the signs inside:
We find that all terms in the numerator which do not
contain the factor h will cancel and we are left with:
That will allow us to factor out an h in the numerator:
Then we can cancel the h's
And we are left with:
Edwin
