anonymous
  • anonymous
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) ~=
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[f^2=2f*f'\]
anonymous
  • anonymous
what is that?
anonymous
  • anonymous
do I plug 9.5 for f?

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anonymous
  • anonymous
do I plug 9.5 for f?
TuringTest
  • TuringTest
\[f'(x)\approx\frac{f(x+\Delta x)-f(x)}{\Delta x}\]\[f(x+\Delta x)\approx f(x)+f'(x)\Delta x\]\[f(9.5)=f(9+0.5)\approx f(9)+f'(9)(0.5)\]
TuringTest
  • TuringTest
(you plug in 0.5 for delta x is the deal)
anonymous
  • anonymous
ok so I just plug in 0.5 and multiply with 9 and I get the answer
anonymous
  • anonymous
right?
TuringTest
  • TuringTest
? what do you think the answer is?
anonymous
  • anonymous
4.5
TuringTest
  • TuringTest
no what is f'(9) ?
anonymous
  • anonymous
0
TuringTest
  • TuringTest
why do you think it's zero no, it's given in the question
anonymous
  • anonymous
answer is 9.5?
TuringTest
  • TuringTest
no, how are you getting these answers?
anonymous
  • anonymous
I thought I was trying to get the derivitave of f'(9)
TuringTest
  • TuringTest
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
anonymous
  • anonymous
so 0.5 x
anonymous
  • anonymous
and then solve
TuringTest
  • TuringTest
I don't know what you mean, show your work please
anonymous
  • anonymous
what I mean is that would put 0.5 for delta then solve w/ x
TuringTest
  • TuringTest
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
anonymous
  • anonymous
do I still need to solve or is that the answer?
TuringTest
  • TuringTest
you still need to substitute in the numbers given in the problem and do the simple arithmetic
TuringTest
  • TuringTest
what is f(9) ? what is f'(9) ? both are given in your very post
anonymous
  • anonymous
i got 112.5
anonymous
  • anonymous
is that right?

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