G9211
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)?



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victorarana
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You could do a linear estimation.

victorarana
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dw:1326783771569:dw

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

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

victorarana
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Do you know what a linear estimation is?

G9211
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No, its f (25) = 3.
and thanks to everyone helping!

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

G9211
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sorry, its f^1

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

victorarana
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Mmm wait a minute.

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

victorarana
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that looks like a vertical line,

victorarana
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like x = 25

G9211
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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

G9211
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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)?

G9211
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would i still approach it the same way Victorarana?

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

G9211
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yes!

victorarana
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Ok you can integrate then.

G9211
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sorry im new to calculus and new to this website, im not entirely sure what you mean :P

victorarana
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Don't worry, let me think

victorarana
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I got it. let me make a draw

G9211
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okay thanks a lot! i appreciate it!

victorarana
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dw:1326784522811:dw

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

victorarana
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and the slope of a tangent line at that point

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

victorarana
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but only at the point near x = 25

victorarana
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Is it clear?

G9211
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Yeah that makes sense! Thank you VERY much :)

victorarana
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then you can do the rest by yourself =)

G9211
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yep, thanks again!

victorarana
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You're welcome