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anonymous

  • 4 years ago

help !!! Given the facts that f(9) = 11 and f'(9) = 3, use the difference quotient to estimate the value of f( 9.5 ). f(9.5) ~=

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  1. anonymous
    • 4 years ago
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    \[f^2=2f*f'\]

  2. anonymous
    • 4 years ago
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    what is that?

  3. anonymous
    • 4 years ago
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    do I plug 9.5 for f?

  4. anonymous
    • 4 years ago
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    do I plug 9.5 for f?

  5. TuringTest
    • 4 years ago
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    \[f'(x)\approx\frac{f(x+\Delta x)-f(x)}{\Delta x}\]\[f(x+\Delta x)\approx f(x)+f'(x)\Delta x\]\[f(9.5)=f(9+0.5)\approx f(9)+f'(9)(0.5)\]

  6. TuringTest
    • 4 years ago
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    (you plug in 0.5 for delta x is the deal)

  7. anonymous
    • 4 years ago
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    ok so I just plug in 0.5 and multiply with 9 and I get the answer

  8. anonymous
    • 4 years ago
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    right?

  9. TuringTest
    • 4 years ago
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    ? what do you think the answer is?

  10. anonymous
    • 4 years ago
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    4.5

  11. TuringTest
    • 4 years ago
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    no what is f'(9) ?

  12. anonymous
    • 4 years ago
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    0

  13. TuringTest
    • 4 years ago
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    why do you think it's zero no, it's given in the question

  14. anonymous
    • 4 years ago
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    answer is 9.5?

  15. TuringTest
    • 4 years ago
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    no, how are you getting these answers?

  16. anonymous
    • 4 years ago
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    I thought I was trying to get the derivitave of f'(9)

  17. TuringTest
    • 4 years ago
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    f'(9) is a constant, so its derivative would be zero we don't need that, we just need the value of f(9), f'(9) and Delta x the first two are given in the problem, and I already told you the value of Delta x

  18. anonymous
    • 4 years ago
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    so 0.5 x

  19. anonymous
    • 4 years ago
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    and then solve

  20. TuringTest
    • 4 years ago
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    I don't know what you mean, show your work please

  21. anonymous
    • 4 years ago
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    what I mean is that would put 0.5 for delta then solve w/ x

  22. TuringTest
    • 4 years ago
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    If you knew how to solve the problem you would have done it rather than explain it, it takes just a moment since I already gave you the formula above Again, starting with the difference quotient:\[f'(x)\approx\frac{f(x+\Delta x)-f(x)}{\Delta x}\]rearranging:\[f(x+\Delta x)\approx f(x)+f'(x)\Delta x\]sub in for a particular point, and not that the difference between this point in question and the one already given is Delta x=0.5\[f(9.5)=f(9+0.5)\approx f(9)+f'(9)(0.5)\]now you have all given information

  23. anonymous
    • 4 years ago
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    do I still need to solve or is that the answer?

  24. TuringTest
    • 4 years ago
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    you still need to substitute in the numbers given in the problem and do the simple arithmetic

  25. TuringTest
    • 4 years ago
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    what is f(9) ? what is f'(9) ? both are given in your very post

  26. anonymous
    • 4 years ago
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    i got 112.5

  27. anonymous
    • 4 years ago
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    is that right?

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