Math Help - Quotient or Product

1. 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.

2. Re: Quotient or Product

Originally Posted by vicarcook
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...

3. 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

4. Re: Quotient or Product

Many thanks. I got the differential right, but missed the trick of just using the numerator = 0.

5. 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

6. Re: Quotient or Product

Originally Posted by biffboy
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.