Thread: Finding Local Maximum & Minimum f(x)=x/(x^2+x+1)

I've been having alot of trouble with this question firstly i took the derivative of it and got (1-x^2)/(x^2+x+1)^2. Now to get the critical numbers i make the top and bottom =0. 1-x^2=0, x=1 Now for (x^2+x+1)^2 do i make (x^2+x+1)=0, x=-1 & (x^2-x-1)=0, x=1.? So from that its increasing from (-infinity,1) and decreasing from (1, infinity). Thats all i got.

If any can redo the question if i made errors it will be much appriciated.

You have correctly differentiated to find:



The denominator has no real roots, since the discriminant is negative. So, you only need test the sign of the numerator on the intervals:



From this, you can find the nature of the two extrema.