Finding the rAnge C3 Help Watch

owl 1996
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Hello,

Can anyone tell me how to find the range of y= 6/x +2x when x is greater than or equal to one but less than or equal to three? Thank you for any help!


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Khallil
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(Original post by owl 1996)
Find the range of f(x) = \frac{6}{x} + 2x, \ 1 \leq x \leq 3
Find f(1), \ f(3) and the derivative at those points: f'(1) and f'(3).

You'll find that the derivative at x=1 is less than 0 and the derivative at x=3 is greater than 0. Since the function is continuous, the derivative must be equal to 0 at a point in the interval \left[ 1, 3 \right]. Find this point.

This should give you all of the information you need to sketch the graph.

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(Original post by m4ths/maths247)
What techniques do you think you could use? (you have a small interval there too which may help....)
Do you think I've given too much of the question away? I haven't explicitly calculated anything but I have outlined most if not all of the method.
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m4ths/maths247
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(Original post by owl 1996)
Hello,

Can anyone tell me how to find the range of y= 6/x +2x when x is greater than or equal to one but less than or equal to three? Thank you for any help!


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What techniques do you think you could use? (you have a small interval there too which may help....)
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owl 1996
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(Original post by Khallil)
Find f(1), \ f(3) and the derivative at those points: f'(1) and f'(3).

You'll find that the derivative at x=1 is less than 0 and the derivative at x=3 is greater than 0. Since the function is continuous, the derivative must be equal to 0 at a point in the interval \left[ 1, 3 \right]. Find this point.

This should give you all of the information you need to sketch the graph.

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Do you think I've given too much of the question away? I haven't explicitly calculated anything but I have outlined most if not all of the method.
The lowest f(x) can be is 4*3^(1/2) . Thank you!


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owl 1996
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(Original post by m4ths/maths247)
What techniques do you think you could use? (you have a small interval there too which may help....)
Thanks


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Khallil
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(Original post by owl 1996)
The lowest f(x) can be is 4*3^(1/2) . Thank you!


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Now you can find the greatest value f can take and that gives you the range.

4\sqrt{3} \leq f(x) \leq \ ?
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