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The curve with equation y=e^2x/4+3e^x has one stationary point.find the exact value of the coordinates of this point

User TWright
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y=(e^(2x))/(4+3e^x)

\implies y'=(2e^(2x)(4+3e^x)-3e^xe^(2x))/((4+3e^x)^2)

\implies y'=(8e^(2x)+3e^(3x))/((4+3e^x)^2)

Stationary points occur where the derivative is zero. The denominator is positive for all
x, so we only need to worry about the numerator.


8e^(2x)+3e^(3x)=e^(2x)(8+3e^x)=0


e^(2x)>0 for all
x, so we can divide through:


8+3e^x=0\implies e^x=-\frac83

But
e^x>0 for all
x\in\mathbb R, so this function has no stationary points...

I suspect there may be a typo in the question.
User Willy Du Preez
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