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) ~=

- anonymous

- schrodinger

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- anonymous

\[f^2=2f*f'\]

- anonymous

what is that?

- anonymous

do I plug 9.5 for f?

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## More answers

- anonymous

do I plug 9.5 for f?

- 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

(you plug in 0.5 for delta x is the deal)

- anonymous

ok so I just plug in 0.5 and multiply with 9 and I get the answer

- anonymous

right?

- TuringTest

?
what do you think the answer is?

- anonymous

4.5

- TuringTest

no
what is f'(9) ?

- anonymous

0

- TuringTest

why do you think it's zero
no, it's given in the question

- anonymous

answer is 9.5?

- TuringTest

no, how are you getting these answers?

- anonymous

I thought I was trying to get the derivitave of f'(9)

- 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

so 0.5 x

- anonymous

and then solve

- TuringTest

I don't know what you mean, show your work please

- anonymous

what I mean is that would put 0.5 for delta then solve w/ x

- 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

do I still need to solve or is that the answer?

- TuringTest

you still need to substitute in the numbers given in the problem and do the simple arithmetic

- TuringTest

what is f(9) ?
what is f'(9) ?
both are given in your very post

- anonymous

i got 112.5

- anonymous

is that right?

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