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    Hello!
    The question is as follows-
    Find the minimum value of y= tanx-8sinx which is given by a value of x between 0 and pi/2

    So firstly I differentiated y=tanx-8sinx. Which gave me dy/dx= sec^2x-8cosx.
    Then I made that = 0, and solved for x
    0=1/cos^2x - 8cosx
    0=cosx(1/cos^3x -8)
    cosx=0
    x=pi/2
    But the limits do not include pi/2, so I discount this value for x.
    1/cos^3x=8
    cosx=(plusorminus)1/2
    x= pi/3 or 2pi/3
    But I managed to get 2 answers, both are wrong.

    The answer is -3root3. So I'm stumped.
    Would love it if you can spot where I went wrong!
    Thanks XD
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    (Original post by Ruineth)
    Hello!
    The question is as follows-
    Find the minimum value of y= tanx-8sinx which is given by a value of x between 0 and pi/2

    So firstly I differentiated y=tanx-8sinx. Which gave me dy/dx= sec^2x-8cosx.
    Then I made that = 0, and solved for x
    0=1/cos^2x - 8cosx
    0=cosx(1/cos^3x -8)
    cosx=0
    x=pi/2
    But the limits do not include pi/2, so I discount this value for x.
    1/cos^3x=8
    cosx=(plusorminus)1/2
    x= pi/3 or 2pi/3
    But I managed to get 2 answers, both are wrong.

    The answer is -3root3. So I'm stumped.
    Would love it if you can spot where I went wrong!
    Thanks XD
    I put a line in bold; from there try putting the right hand side as one fraction.
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    (Original post by Ruineth)
    Hello!
    The question is as follows-
    Find the minimum value of y= tanx-8sinx which is given by a value of x between 0 and pi/2

    So firstly I differentiated y=tanx-8sinx. Which gave me dy/dx= sec^2x-8cosx.
    Then I made that = 0, and solved for x
    0=1/cos^2x - 8cosx
    0=cosx(1/cos^3x -8)
    cosx=0
    x=pi/2
    But the limits do not include pi/2, so I discount this value for x.
    1/cos^3x=8
    cosx=(plusorminus)1/2
    x= pi/3 or 2pi/3
    But I managed to get 2 answers, both are wrong.

    The answer is -3root3. So I'm stumped.
    Would love it if you can spot where I went wrong!
    Thanks XD
    It looks like you've done it correctly, it's just asking for the minimum value of y.. soo..
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    (Original post by Andy98)
    I put a line in bold; from there try putting the right hand side as one fraction.
    0= (1-8cos^3)/cos^2x
    But if the top = 0, then I get the same answers as I got before?
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    (Original post by SeanFM)
    It looks like you've done it correctly, it's just asking for the minimum value of y.. soo..
    Ohhhh yeahhh - whoops, would help if I read the question properly

    (Original post by Ruineth)
    0= (1-8cos^3)/cos^2x
    But if the top = 0, then I get the same answers as I got before?
    Sean's right, you've got x - it wants y
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    (Original post by Andy98)
    Ohhhh yeahhh - whoops, would help if I read the question properly



    Sean's right, you've got x - it wants y
    Omg.
    I should not be allowed to sit exams XD
    Thanks both of you! Hahaha
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    (Original post by Ruineth)
    Omg.
    I should not be allowed to sit exams XD
    Thanks both of you! Hahaha
    Hey, I read it wrong too
 
 
 
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