Question

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

Answer 1

that one is cube

Answer 2

to get f(x+h), just replace all 'x' in f(x) by 'x+h'

Answer 3

i don't understand

Answer 4

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

Answer 5

so, can you try replacing 'x' in f(x) by x+h for your question,
x^3+4x ?

Answer 6

x^3+4x+h

Answer 7

\[f(\color{#C00}x) = \color{#C00}x^3 + 4\color{#c00}x \\ f(\color{#C00}h) = \color{#c00}h^3 + 4 \color{#C00}h \\ \vdots \]

Answer 8

?????? i'm not sure

Answer 9

wherever you 'see' x, just replace it by 'x+h'
one more try , maybe ?

Answer 10

u want 1 more example ?

Answer 11

(x+h)^3+4(x+h)

Answer 12

\(\checkmark \)

Answer 13

is that right now?????

Answer 14

That's it! Expand

Answer 15

now, can you expand (x+h)^3 ?

Answer 16

use \((a+b)^3 = a^3+3a^2b+3ab^2+b^3\)

Answer 17

Just replace \(a\) by \(x\) and \(b\) by \(h\).

Answer 18

x^3+2hx^2+2hx+hx^2+2h^2x+2h^2

Answer 19

Uh, that is expanded a little too much.

Answer 20

x^3+3hx^2+2h^x+2h^2+2hx

Answer 21

where did h^3 go ?

Answer 22

wheere will i get that h^3

Answer 23

you'll have only 4 terms from that formula, right ?

Answer 24

Four completely simplified terms.

Answer 25

\((a+b)^3 = a^3+3a^2b+3ab^2+b^3\)
from the last term b^3 of above

Answer 26

i'm confused now

Answer 27

Why?

Answer 28

x^3+3x^h+3xh^2+h^3

Answer 29

yes!

Answer 30

is that right now. . .

Answer 31

x^3+3x^2h+3xh^2+h^3

Answer 32

then?

Answer 33

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...

Answer 34

(x+h) can be factored, but not required...

Answer 35

thanks

Answer 36

welcome ^_^