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    Name:  IMG_1794.jpg
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Size:  443.8 KBCan someone help me with 3(iv)?
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    Divide through by x as a first step...
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    (Original post by DFranklin)
    Divide through by x as a first step...
    wouldn't you move ax to the left so that e^x - ax=0, and then differentiate?
    thats what I did but I don't know what to do next
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    (Original post by SWISH99)
    wouldn't you move ax to the left so that e^x - ax=0, and then differentiate?
    No I wouldn't. Why do you think that would help?
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    (Original post by DFranklin)
    No I wouldn't. Why do you think that would help?
    thats what I did for question ii)
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    (Original post by SWISH99)
    thats what I did for question ii)
    Yes, and when you did it for (ii), you got e^x - 1, which you deduced was >=0 for x >=0. However, note that e^x - 1 equals 0 when x = 0. So this is already the best you can do using this simple method - if you take \alpha &gt; 1 then \dfrac{d}{dx}(e^x - \alpha x) = e^x - \alpha which is < 0 when x = 0.
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    (Original post by DFranklin)
    Yes, and when you did it for (ii), you got e^x - 1, which you deduced was >=0 for x >=0. However, note that e^x - 1 equals 0 when x = 0. So this is already the best you can do using this simple method - if you take \alpha &gt; 1 then \dfrac{d}{dx}(e^x - \alpha x) = e^x - \alpha which is < 0 when x = 0.
    I see what you're saying. So how would dividing by x help?
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    what year are yo in?
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    (Original post by SWISH99)
    I see what you're saying. So how would dividing by x help?
    Have a think about what "the biggest value \alpha s.t. \dfrac{e^x}{x} \geq \alpha for x >=0" means in terms of the graph of \dfrac{e^x}{x}.

    (I don't want to spell this out for you, this is the kind of thing you need to get used to understanding on your own).
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    (Original post by SalvadorMendes)
    what year are yo in?
    why?
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    (Original post by DFranklin)
    Have a think about what "the biggest value \alpha s.t. \dfrac{e^x}{x} \geq \alpha for x >=0" means in terms of the graph of \dfrac{e^x}{x}.

    (I don't want to spell this out for you, this is the kind of thing you need to get used to understanding on your own).
    Oh I think I get what you mean. Differentiating e^x/x in order to find the minimum point?
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    (Original post by SWISH99)
    Oh I think I get what you mean. Differentiating e^x/x in order to find the minimum point?
    Yes, that's right
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    this is complicated and I'm in year 10 and I'm getting really scared
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    (Original post by SalvadorMendes)
    this is complicated and I'm in year 10 and I'm getting really scared
    This is undergrad, you won't have to worry about limits for a while. (the earliest you'll encounter them is probably year 13)
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    oh thank god
 
 
 
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