keneisha
What is f(x+h) for the function f(x)=x^3+4x?



This Question is Closed

keneisha
Best Response
You've already chosen the best response.
2
that one is cube

hartnn
Best Response
You've already chosen the best response.
0
to get f(x+h), just replace all 'x' in f(x) by 'x+h'

keneisha
Best Response
You've already chosen the best response.
2
i don't understand

hartnn
Best Response
You've already chosen the best response.
0
example if f(x) = x^2+10 x
f(x+h) will be (x+h)^2 + 10(x+h)
note that i have replaced ALL 'x' in f(x) by x+h

hartnn
Best Response
You've already chosen the best response.
0
so, can you try replacing 'x' in f(x) by x+h for your question,
x^3+4x ?

keneisha
Best Response
You've already chosen the best response.
2
x^3+4x+h

ParthKohli
Best Response
You've already chosen the best response.
0
\[f(\color{#C00}x) = \color{#C00}x^3 + 4\color{#c00}x \\ f(\color{#C00}h) = \color{#c00}h^3 + 4 \color{#C00}h \\ \vdots \]

keneisha
Best Response
You've already chosen the best response.
2
?????? i'm not sure

hartnn
Best Response
You've already chosen the best response.
0
wherever you 'see' x, just replace it by 'x+h'
one more try , maybe ?

hartnn
Best Response
You've already chosen the best response.
0
u want 1 more example ?

keneisha
Best Response
You've already chosen the best response.
2
(x+h)^3+4(x+h)

hartnn
Best Response
You've already chosen the best response.
0
\(\checkmark \)

keneisha
Best Response
You've already chosen the best response.
2
is that right now?????

ParthKohli
Best Response
You've already chosen the best response.
0
That's it! Expand

hartnn
Best Response
You've already chosen the best response.
0
now, can you expand (x+h)^3 ?

hartnn
Best Response
You've already chosen the best response.
0
use \((a+b)^3 = a^3+3a^2b+3ab^2+b^3\)

ParthKohli
Best Response
You've already chosen the best response.
0
Just replace \(a\) by \(x\) and \(b\) by \(h\).

keneisha
Best Response
You've already chosen the best response.
2
x^3+2hx^2+2hx+hx^2+2h^2x+2h^2

ParthKohli
Best Response
You've already chosen the best response.
0
Uh, that is expanded a little too much.

keneisha
Best Response
You've already chosen the best response.
2
x^3+3hx^2+2h^x+2h^2+2hx

hartnn
Best Response
You've already chosen the best response.
0
where did h^3 go ?

keneisha
Best Response
You've already chosen the best response.
2
wheere will i get that h^3

hartnn
Best Response
You've already chosen the best response.
0
you'll have only 4 terms from that formula, right ?

ParthKohli
Best Response
You've already chosen the best response.
0
Four completely simplified terms.

hartnn
Best Response
You've already chosen the best response.
0
\((a+b)^3 = a^3+3a^2b+3ab^2+b^3\)
from the last term b^3 of above

keneisha
Best Response
You've already chosen the best response.
2
i'm confused now

ParthKohli
Best Response
You've already chosen the best response.
0
Why?

keneisha
Best Response
You've already chosen the best response.
2
x^3+3x^h+3xh^2+h^3

hartnn
Best Response
You've already chosen the best response.
0
yes!

keneisha
Best Response
You've already chosen the best response.
2
is that right now. . .

hartnn
Best Response
You've already chosen the best response.
0
x^3+3x^2h+3xh^2+h^3

keneisha
Best Response
You've already chosen the best response.
2
then?

hartnn
Best Response
You've already chosen the best response.
0
so, you have
(x+h)^3+4(x+h)
=x^3+3x^2h+3xh^2+h^3 +4x+4h
i think no further simplification possible, thats your final answer...

hartnn
Best Response
You've already chosen the best response.
0
(x+h) can be factored, but not required...

keneisha
Best Response
You've already chosen the best response.
2
thanks

hartnn
Best Response
You've already chosen the best response.
0
welcome ^_^