## G9211 3 years ago Suppose that f is a function with f (25) = 61 and f (25) = 3. If you have no further information, what is your best estimate of f(26.5)?

1. victorarana

You could do a linear estimation.

2. victorarana

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3. rivermaker

I think there is a typo in the question. Is it f(26) = 3

4. Hero

You only have two points. You have no choice but to consider linear estimation.

5. victorarana

Do you know what a linear estimation is?

6. G9211

No, its f (25) = 3. and thanks to everyone helping!

7. rivermaker

f(25) = 3 and f(25) = 61???

8. G9211

sorry, its f^1

9. victorarana

remember that you can graph a line with two points. like the picture I drawn

10. victorarana

Mmm wait a minute.

11. rivermaker

This is odd. The question is wrong and the answer is giiven and gets a medal too! :-)

12. victorarana

that looks like a vertical line,

13. victorarana

like x = 25

14. G9211

okay i'll try reposting the question too, if anyone else is confused. I copied it from the file im working on and pasted it so it took away the powers

15. G9211

Suppose that f is a function with f (25) = 61 and f^1 (25)= 3. If you have no further information, what is your best estimate of f(26.5)?

16. G9211

would i still approach it the same way Victorarana?

17. victorarana

mmm with the f^1 you mean derivative i suppose?

18. G9211

yes!

19. victorarana

Ok you can integrate then.

20. G9211

sorry im new to calculus and new to this website, im not entirely sure what you mean :P

21. victorarana

Don't worry, let me think

22. victorarana

I got it. let me make a draw

23. G9211

okay thanks a lot! i appreciate it!

24. victorarana

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25. victorarana

that is the information we have. a point (25,f(25))

26. victorarana

and the slope of a tangent line at that point

27. victorarana

like we told you before, you can aproximate the value of the function with a straight line

28. victorarana

but only at the point near x = 25

29. victorarana

Is it clear?

30. G9211

Yeah that makes sense! Thank you VERY much :)

31. victorarana

then you can do the rest by yourself =)

32. G9211

yep, thanks again!

33. victorarana

You're welcome