Hey im stuck on this, can ne1 help; find the stationary points & if a max/min y=1/2x+1 - 1/(2x+1)2, thanx?

Question

hey this is due in tomorrow, so any help seriously appreciated, thanx

yes it was written like that, the problem was that i knew the principle of how to do it i just kept getting really stuck when working it out,

Answer 1

Please clarify how the function is written. Is it

1/(2x+1) - 1/[(2x+1)2]?

In any case, what you do is differentiate the function, and set it equal to zero to find the critical points, where a max or min MAY occur.

To determine if a critical point really is a max or a min, you can either:
1) compute the second derivative and plug in the critical point. If it's positive, it's a min, if it's negative, it's a max, if it's zero, then it's inconclusive
2) determine whether the first derivative changes sign at the critical point, by plugging in x-values on either side of the point. If it changes from negative to positive as x increases, it's a min. If it changes sign from positive to negative, it's a max. If there's no sign change, then it's neither.

Answer 2

y'= one million/2 (4x-one million)^{-one million/2} 4 - 9/2(4x-one million)^{-3/2} = [4(4x-one million) -9]/(2(4x-one million)^{3/2}) and that's =- if 4(4x-one million) -9=0 so 16x-4-9=0 16x=thirteen x=thirteen/sixteen if x=one million, then y'>0 and if x=0, then y'<0 so the severe factor is a (interior of sight) minimum