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Math Help - Quotient or Product

  1. #1
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    Quotient or Product

    I am trying to help an A level pupil.
    The question is:-
    Find the stationary point on the curve y = e^x / sq. root x ; and say whether it is a min or max.

    I have tried this both ways and keep getting the answer 2/3 and min. value. It seems I'm missing something at the point where you take logs, but I can't see it.
    I know that graphically the answer is 1/2 and min. value.
    Can anyone show me the corect algebraic procedure and get the answer 1/2.
    Thanks.
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  2. #2
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    Re: Quotient or Product

    Quote Originally Posted by vicarcook View Post
    I am trying to help an A level pupil.
    The question is:-
    Find the stationary point on the curve y = e^x / sq. root x ; and say whether it is a min or max.

    I have tried this both ways and keep getting the answer 2/3 and min. value. It seems I'm missing something at the point where you take logs, but I can't see it.
    I know that graphically the answer is 1/2 and min. value.
    Can anyone show me the corect algebraic procedure and get the answer 1/2.
    Thanks.
    Please show what you got for dy/dx...
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  3. #3
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    Re: Quotient or Product

    Usng quotient rule dy/dx=(rootx*e^x-e^x*1/(2rootx) divided by (rootx)^2

    For dy/dx=0 we require numerator to be 0 Multiply both sides by rootx getting xe^x -e^x1/2=0 e^x(x-1/2)=0 x=1/2
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  4. #4
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    Re: Quotient or Product

    Many thanks. I got the differential right, but missed the trick of just using the numerator = 0.
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  5. #5
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    Re: Quotient or Product

    I should also have mentioned that when we solve the numerator =0 we should check that we don't get a value which would also make the denominator =0
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  6. #6
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    Re: Quotient or Product

    Quote Originally Posted by biffboy View Post
    I should also have mentioned that when we solve the numerator =0 we should check that we don't get a value which would also make the denominator =0
    Point taken, many thanks. I won't forget this one in a hurry.
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