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Question 458813:
For the given function, find
f(x+h)-f(x)
———————————
h
f(x) = x² - 8x
A) 2x - 8 + h
B) 2xh+h2-8h-16w/h
C) 2x + h
D) 2x + 8 + h
My brain doesn't even know where to begin on this one..
tho for some reason my brain thinks the answer is b..
but doesn't know how?
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
For the given function, find
f(x+h) - f(x)
—————————————
h
f(x) = x² - 8x
===================================================
To find
f(x+h) - f(x)
—————————————
h
1. First find f(x+h)
f(x) = x² - 8x
That is, replace every x by (x+h), and get
f(x+h) = (x+h)² - 8(x+h)
Now simplify the right side:
f(x+h) = (x+h)(x+h) - 8x - 8h
f(x+h) = x² + hx + hx + h² - 8x - 8h
f(x+h) = x² + 2hx + h² - 8x - 8h
2. Now substitute x² + 2hx + h² - 8x - 8h for f(x+h) in
f(x+h) - f(x)
—————————————
h
and get
x² + 2hx + h² - 8x - 8h - f(x)
—————————————————————————————
h
3. Now substitute (x² - 8x) for f(x) in that:
x² + 2hx + h² - 8x - 8h - (x² - 8x)
——————————————————————————————————
h
Remove the parentheses in the numerator:
x² + 2hx + h² - 8x - 8h - x² + 8x
—————————————————————————————————
h
Now the x² and the -x² cancel, and
the -8x and the +8x cancel, giving:
2hx + h² - 8h
—————————————
h
4. Now factor out h in the numerator:
h(2x + h - 8)
—————————————
h
5. Now cancel the h factor in the numerator and
the denominator and get:
2x + h - 8
Now if you will swap the last two terms you will
get choice A).
A) 2x - 8 + h
Edwin
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