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keneisha

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

  • one year ago
  • one year ago

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  1. keneisha
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    that one is cube

    • one year ago
  2. hartnn
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    to get f(x+h), just replace all 'x' in f(x) by 'x+h'

    • one year ago
  3. keneisha
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    i don't understand

    • one year ago
  4. hartnn
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    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

    • one year ago
  5. hartnn
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    so, can you try replacing 'x' in f(x) by x+h for your question, x^3+4x ?

    • one year ago
  6. keneisha
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    x^3+4x+h

    • one year ago
  7. ParthKohli
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    \[f(\color{#C00}x) = \color{#C00}x^3 + 4\color{#c00}x \\ f(\color{#C00}h) = \color{#c00}h^3 + 4 \color{#C00}h \\ \vdots \]

    • one year ago
  8. keneisha
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    ?????? i'm not sure

    • one year ago
  9. hartnn
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    wherever you 'see' x, just replace it by 'x+h' one more try , maybe ?

    • one year ago
  10. hartnn
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    u want 1 more example ?

    • one year ago
  11. keneisha
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    (x+h)^3+4(x+h)

    • one year ago
  12. hartnn
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    \(\checkmark \)

    • one year ago
  13. keneisha
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    is that right now?????

    • one year ago
  14. ParthKohli
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    That's it! Expand

    • one year ago
  15. hartnn
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    now, can you expand (x+h)^3 ?

    • one year ago
  16. hartnn
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    use \((a+b)^3 = a^3+3a^2b+3ab^2+b^3\)

    • one year ago
  17. ParthKohli
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    Just replace \(a\) by \(x\) and \(b\) by \(h\).

    • one year ago
  18. keneisha
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    x^3+2hx^2+2hx+hx^2+2h^2x+2h^2

    • one year ago
  19. ParthKohli
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    Uh, that is expanded a little too much.

    • one year ago
  20. keneisha
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    x^3+3hx^2+2h^x+2h^2+2hx

    • one year ago
  21. hartnn
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    where did h^3 go ?

    • one year ago
  22. keneisha
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    wheere will i get that h^3

    • one year ago
  23. hartnn
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    you'll have only 4 terms from that formula, right ?

    • one year ago
  24. ParthKohli
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    Four completely simplified terms.

    • one year ago
  25. hartnn
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    \((a+b)^3 = a^3+3a^2b+3ab^2+b^3\) from the last term b^3 of above

    • one year ago
  26. keneisha
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    i'm confused now

    • one year ago
  27. ParthKohli
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    Why?

    • one year ago
  28. keneisha
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    x^3+3x^h+3xh^2+h^3

    • one year ago
  29. hartnn
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    yes!

    • one year ago
  30. keneisha
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    is that right now. . .

    • one year ago
  31. hartnn
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    x^3+3x^2h+3xh^2+h^3

    • one year ago
  32. keneisha
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    then?

    • one year ago
  33. hartnn
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    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...

    • one year ago
  34. hartnn
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    (x+h) can be factored, but not required...

    • one year ago
  35. keneisha
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    thanks

    • one year ago
  36. hartnn
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    welcome ^_^

    • one year ago
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