anonymous
  • anonymous
What is f(x+h) for the function f(x)=x^3+4x?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
that one is cube
hartnn
  • hartnn
to get f(x+h), just replace all 'x' in f(x) by 'x+h'
anonymous
  • anonymous
i don't understand

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hartnn
  • hartnn
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
  • hartnn
so, can you try replacing 'x' in f(x) by x+h for your question, x^3+4x ?
anonymous
  • anonymous
x^3+4x+h
ParthKohli
  • ParthKohli
\[f(\color{#C00}x) = \color{#C00}x^3 + 4\color{#c00}x \\ f(\color{#C00}h) = \color{#c00}h^3 + 4 \color{#C00}h \\ \vdots \]
anonymous
  • anonymous
?????? i'm not sure
hartnn
  • hartnn
wherever you 'see' x, just replace it by 'x+h' one more try , maybe ?
hartnn
  • hartnn
u want 1 more example ?
anonymous
  • anonymous
(x+h)^3+4(x+h)
hartnn
  • hartnn
\(\checkmark \)
anonymous
  • anonymous
is that right now?????
ParthKohli
  • ParthKohli
That's it! Expand
hartnn
  • hartnn
now, can you expand (x+h)^3 ?
hartnn
  • hartnn
use \((a+b)^3 = a^3+3a^2b+3ab^2+b^3\)
ParthKohli
  • ParthKohli
Just replace \(a\) by \(x\) and \(b\) by \(h\).
anonymous
  • anonymous
x^3+2hx^2+2hx+hx^2+2h^2x+2h^2
ParthKohli
  • ParthKohli
Uh, that is expanded a little too much.
anonymous
  • anonymous
x^3+3hx^2+2h^x+2h^2+2hx
hartnn
  • hartnn
where did h^3 go ?
anonymous
  • anonymous
wheere will i get that h^3
hartnn
  • hartnn
you'll have only 4 terms from that formula, right ?
ParthKohli
  • ParthKohli
Four completely simplified terms.
hartnn
  • hartnn
\((a+b)^3 = a^3+3a^2b+3ab^2+b^3\) from the last term b^3 of above
anonymous
  • anonymous
i'm confused now
ParthKohli
  • ParthKohli
Why?
anonymous
  • anonymous
x^3+3x^h+3xh^2+h^3
hartnn
  • hartnn
yes!
anonymous
  • anonymous
is that right now. . .
hartnn
  • hartnn
x^3+3x^2h+3xh^2+h^3
anonymous
  • anonymous
then?
hartnn
  • hartnn
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
  • hartnn
(x+h) can be factored, but not required...
anonymous
  • anonymous
thanks
hartnn
  • hartnn
welcome ^_^

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