## 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) ~=

1. anonymous

$f^2=2f*f'$

2. anonymous

what is that?

3. anonymous

do I plug 9.5 for f?

4. anonymous

do I plug 9.5 for f?

5. 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)$

6. TuringTest

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

7. anonymous

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

8. anonymous

right?

9. TuringTest

? what do you think the answer is?

10. anonymous

4.5

11. TuringTest

no what is f'(9) ?

12. anonymous

0

13. TuringTest

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

14. anonymous

15. TuringTest

no, how are you getting these answers?

16. anonymous

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

17. 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

18. anonymous

so 0.5 x

19. anonymous

and then solve

20. TuringTest

21. anonymous

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

22. 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

23. anonymous

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

24. TuringTest

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

25. TuringTest

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

26. anonymous

i got 112.5

27. anonymous

is that right?