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keneisha

  • one year ago

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

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  1. keneisha
    • one year ago
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    that one is cube

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

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

  4. hartnn
    • one year ago
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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  27. ParthKohli
    • one year ago
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    Why?

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

  29. hartnn
    • one year ago
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    yes!

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

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

  32. keneisha
    • one year ago
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    then?

  33. hartnn
    • one year ago
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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...

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

  35. keneisha
    • one year ago
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    thanks

  36. hartnn
    • one year ago
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    welcome ^_^

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