# f(x) = -x^3 evaluating for f(a+h)

• June 26th 2010, 10:54 PM
superduper1
f(x) = -x^3 evaluating for f(a+h)
When I evaluate f(x)= -x^3 for f(a+h)

How is it suppose to look? I'm not sure what to do with the negative in front of the x

f(a+h) = -[(a+h)(a+h)(a+h)]

or

f(a+h) = [(-a-h)(-a-h)(-a-h)]
• June 26th 2010, 11:12 PM
CaptainBlack
Quote:

Originally Posted by superduper1
When I evaluate f(x)= -x^3 for f(a+h)

How is it suppose to look? I'm not sure what to do with the negative in front of the x

f(a+h) = -[(a+h)(a+h)(a+h)]

or

f(a+h) = [(-a-h)(-a-h)(-a-h)]

$\displaymaths f(x)=-x^3$

means:

$\displaymaths f(x)=-(x^3)$

so here you want:

$f(x+h)=-( (x+h)^3)=-(x^3+3x^2h+3xh^2+h^3)=-x^3-3x^2h-3xh^2-h^3$

CB
• June 27th 2010, 12:35 AM
superduper1
I'm not sure what I'm doing wrong. The answer I get is incorrect.
f(x) = -x^3
evaluate for f(a+h)-f(a) / h

f-(x^3)= -a^3-3a^3h-3ah^2-h^3
Then when I evaluate for f(a) I get:
f(a) = -a^3

After the -a^3 subtract each other out...I factor out an h from the numerator to cancel out an h from the denominator and get:
-3a^3 - 3ah-h^2
• June 27th 2010, 12:45 AM
CaptainBlack
Quote:

Originally Posted by superduper1
I'm not sure what I'm doing wrong. The answer I get is incorrect.
f(x) = -x^3
evaluate for f(a+h)-f(a) / h

f-(x^3)= -a^3-3a^3h-3ah^2-h^3
Then when I evaluate for f(a) I get:
f(a) = -a^3

After the -a^3 subtract each other out...I factor out an h from the numerator to cancel out an h from the denominator and get:
-3a^3 - 3ah-h^2

You should get:

$-3a^2-3ah-h^2$

CB
• June 27th 2010, 05:21 AM
HallsofIvy
Quote:

Originally Posted by superduper1
I'm not sure what I'm doing wrong. The answer I get is incorrect.
f(x) = -x^3
evaluate for f(a+h)-f(a) / h

f-(x^3)= -a^3-3a^3h-3ah^2-h^3

Probably a typo. The second term should be "-3a^2h", not "-3a^3h".

Quote:

Then when I evaluate for f(a) I get:
f(a) = -a^3

After the -a^3 subtract each other out...I factor out an h from the numerator to cancel out an h from the denominator and get:
-3a^3 - 3ah-h^2
you continued your typo- this should be -3a^2- 3ah- h^2