Let
f(x)=(x−2)2
. Find the average rate of change of
f(x)
with respect to
x
from
x=a
to
x=a+h
if
h≠0
. Simplify your answer as much as possible.

Question

Let 
f(x)=(x−2)2
. Find the average rate of change of 
f(x)
 with respect to 
x
 from 
x=a
 to 
x=a+h
if 
h≠0
. Simplify your answer as much as possible.

anonymous · Answer

Not getting the right answer again

anonymous · Answer

your job is to compute 
$$\frac{f(a+h)-f(a)}{h}$$ rigth?

anonymous · Answer

except for the denominator i have a+h-(a)

anonymous · Answer

in this case 
$$f(x)=(x-2)^2=x^2-4x+4$$ so compute 
$$\frac{(a+h)^2-4(a+h)+4-(a^2-4a+4)}{h}$$ a bunch of algebra now

anonymous · Answer

I got -6a+h+4

anonymous · Answer

which is wrong

anonymous · Answer

it is clear than a + h - a = h rigtht?

anonymous · Answer

o yeah... nevermind then

anonymous · Answer

but yeah, i get how to do it. just getting the wrong answer for some reason.

anonymous · Answer

yes that is incorrect. you need to expand in the numerator and get 
$$\frac{a^2+2ah+h^2-4a-4h+4-a^2+4a-4}{h}=\frac{2ah-4h+h^2}{h}=2a-4+h$$

anonymous · Answer

why is the numerator (towards the end) PLUS 4a and MINUS 4 instead of the opposite thing (which is what I had).

anonymous · Answer

*?

anonymous · Answer

because it is 
$$-f(a)$$ so you have to subtract the whole thing.
in other words if 
$$f(a)=a^2-4a+4$$ then 
$$-f(a)=-(a^2-4a+4)=-a^2+4a-4$$

anonymous · Answer

that always confuses me because i just think of it as a minus sign. i need to start putting everything in parenthesis. 

THANKS