I'm struggling with this question - I think I'm ok with the calculus its just the maniplutaion. Anyway, your help and guidence would be very much appreciated.
The equ. of a curve is (6y^2) = (e^x)(y^3) - 2e^4x.
Given that (a,b) is the point on the curve at which dy/dx = 0,
show that b = 2e^a
By substituting into the equ. obtain a further relationship between a and b, and hence find the values of a and b.
So by implicit diff. and rearranging
(e^x(y^3 - (8e^3x)) / 3y(4 - (e^x)y)) = 0
I'm not really sure how to show the rest though..
can anyone offer some help?