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Evaluating Derivatives

Started by bioagentX Apr 17, 2004 at 10:26 AM 12 replies 900+ views

Original Post

Apr 17, 2004 at 10:26 AM

I know that if f(x) = tan(2x) then f''(x) = 2sec^2(2x). I''m wondering what that value is evaluated at pi/6. In other words, I''m looking for f''(pi/6). I keep getting a value of 8, but apparently that is wrong. Could someone please check my answer, I left my calculator at school. Thx, --BioX

twix

111

twix

Apr 17, 2004 at 10:30 AM

8 is correct, I would think.

Muzzafarath

Apr 17, 2004 at 10:33 AM

If you are able to write this, you obviously have access to a computer, which surely is capable of evaluating trigonometric functions...

Samith

305

Samith

Apr 17, 2004 at 1:03 PM

sec = 1/cos theta right? Then sec² would be 1/cos theta*1/cos theta. Using that I get the answer to be 2.6666666 (You know, two and two thirds.)

I don''t know if I''m right though.

bioagentX

Author

bioagentX

Apr 17, 2004 at 1:40 PM

I don''t know that your answer is right because remember the cos(2 * pi/6) = cos(pi/3) = (1/2). (1/2)^2 = 1/4. That''s what I get and 2/(1/4) = 8, which is the answer I get.

Samith

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Samith

Apr 17, 2004 at 4:53 PM

Oh yeah, Pi is 180 degrees, not 90. Dammit. Well, now I get 8 just like the rest of you.

higherspeed

Apr 17, 2004 at 5:07 PM

It's late and I haven't touched trig functions for a while outside analysis, but from a geometrical and evaluational point of view, it looks like it should be negative to me.

[edited by - Higherspeed on April 17, 2004 6:08:55 PM]

Thunder_Hawk

Apr 17, 2004 at 5:16 PM

quote:
Original post by higherspeed
It''s late and I haven''t touched trig functions for a while outside analysis, but from a geometrical and evaluational point of view, it looks like it should be negative to me.

[edited by - Higherspeed on April 17, 2004 6:08:55 PM]

The derivative of tangent can never be negative. Look at the graph of tangent; it''s either increasing or undefined no matter what.

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higherspeed

Apr 17, 2004 at 7:29 PM

Ha! Good point! Exam on Wednesday.......

I think geometrically I mixed up my functions and when evaluating I missed the square. Oh well at least doing just straight maths, actually evaluating things comes up relatively rarely. So I''ll leave that to the physicists.

JuNC

Apr 18, 2004 at 3:09 AM

Working in radians the answer is 8, working in degrees it is approx 2.00067 (lazily on my calculator

Zipster

511

Zipster

Apr 18, 2004 at 3:23 AM

Never work in degrees. I can''t stress how important it is to think in radians, because everything in math is about radians. Degrees is just what they teach beginning geometry students so they have some sort of grasp of trigonometry, but it won''t do you much good beyond that.

JuNC

Apr 18, 2004 at 8:00 AM

Who are you telling that? I point it out since we have no idea which system the OP is working in and this would explain why his answer of 8 is ''wrong''.

Zipster

511

Zipster

Apr 19, 2004 at 1:30 AM

It was just a general remark on my crusade towards the eradication of degrees (j/k

). But it''s quite apparent everything here is in radians, for multiple reasons.

Also, we have no idea why the OP thinks 8 is "apparently wrong." Quite the contrary, as we''ve all done the calculations and came up with 8 as the correct solution. Unless we all did something wrong. Which I suppose is possible, but not probable.

grhodes_at_work

Mod

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grhodes_at_work

Apr 20, 2004 at 8:05 AM

Thread closing due to homework policy. Please check the Forum FAQ for links to homework sites.

Graham Rhodes
Principal Scientist
Applied Research Associates, Inc.

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