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LotusWings

  • 2 years ago

24: find Point of Inflection and discuss concavity of graph of func. 40: find all relative extrema, use 2nd derivative test where applicable. 58: Water is running into the vase shown @ a constant rate. (a) graph depth of water in vase as a function of time. (b) Does the function have any Extrema? Explain. (c) Interpret the PI (Point of Inflection) of the graph of d.

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  1. LotusWings
    • 2 years ago
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    My work:

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  2. LotusWings
    • 2 years ago
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    @Shadowys can you help please? :O

  3. LotusWings
    • 2 years ago
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    Or anyone really :P

  4. Shadowys
    • 2 years ago
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    lol, um, meanwhile, can you type the original eq.?

  5. LotusWings
    • 2 years ago
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    okay

  6. LotusWings
    • 2 years ago
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    #24: f(x) = sinx+cosx [0, 2Pi] #40: f(x) 2sinx + cos2x [0, 2Pi] I think mostly i'm having issues with just finding the derivative of trig functions. Oh, and my friend helped me with number 58 so it's all cool.

  7. Shadowys
    • 2 years ago
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    for question 40, for the test, you let f'(x) = 0 and solve for x. then, you apply the x-values into f''(x) to test for maxima or minima

  8. Shadowys
    • 2 years ago
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    point of inflexion in 24 is found by letting f''(x)=0. also, you'll need the double angle formulas.

  9. LotusWings
    • 2 years ago
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    yeah, i know how to = 0 but I don't know how to solve the trig to find the x :(

  10. LotusWings
    • 2 years ago
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    |dw:1354600377935:dw|

  11. Shadowys
    • 2 years ago
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    lol okay, i'll do one as an example. \(-sin x- cos x=0\) \(cos x+ sin x=0\) applying the \(Rcos(x-\alpha)\) form, where \(R=\sqrt{1+1}\), \(\alpha = tan^{-1} 1=\pi/4\) \(\sqrt2 cos (x-\pi/4)=0\) solve for x.

  12. LotusWings
    • 2 years ago
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    i don't think i've ever seen the Rcos(x−α) form before. :O

  13. Shadowys
    • 2 years ago
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    hmm, another way is letting sin x = cos(pi\2 -x) but this is much more complicated, but yes, this is the way to solve these type of eqs. for angles with the same cosine, i.e. \(\cos \theta= \cos \alpha\),\( \theta = 2n\pi \pm \alpha\)

  14. LotusWings
    • 2 years ago
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    okay, thanks for your help!

  15. Shadowys
    • 2 years ago
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    you're welcome :)

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