Please Help! I need to find the difference quotient for (x+h) – f(x) / h for 2 – x^2.?

Question

Please Help! I need to find the difference quotient for.

f(x+h) – f(x)
----------------
h

for 2 – x^2.

Answer 1

Ok strictly you meant the difference quotient for
(f(x+h) – f(x))/h
for f(x) = 2 – x²

So f(x) = 2 – x², f(x+h) = 2 – (x+h)² = 2 – x² +2xh –h²

Then (f(x+h) – f(x))/h = [(2 – x² +2xh –h²) –(2 – x²) ] /h
= [2xh –h²] /h
= 2x –h

And you probably want f'(x) = Lim as h->0 (f(x+h) – f(x))/h
=2x

Answer 2

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Answer 3

f(x) = 2 - x²
f(x+h) = 2 - (x+h)² = 2 - x² - 2hx - h²
so the top becomes

2 - x² - 2hx - h² - 2 + x² = -2hx - h²,

and that makes the quotient

[-2hx - h²] / h = -2x + h

and of course, as h→0, the limit becomes -2x.

Answer 4

your asking the impossible.
hehe well, to me it is.