find the absolute maximum and absolute minimum values of f on the given interval
f(x)=ln(x^2+x+1)

[-1,1]

Question

find the absolute maximum and absolute minimum values of f on the given interval 
f(x)=ln(x^2+x+1) 

[-1,1]

anonymous · Answer

calculus or graph?

anonymous · Answer

Uhm, calculus.

anonymous · Answer

ok i guess we can take the derivative, set it equal to zero and solve 
there is probably an easier way, but this will certainly do it

anonymous · Answer

the derivative is $\frac{2x+1}{x^2+x+1}$
note that the denominator is never zero, so we don't have to worry about that one

anonymous · Answer

set the numerator equal to zero and solve (in your  head) you get $x=-\frac{1}{2}$ also knows as the first coordinate of the vertex of $x^2+x+1$ 
that will give you the min
to find the max, check the right hand endpoints of the interval

anonymous · Answer

that is, compute $f(-1),f(1)$ and $f(\frac{1}{2})$ the smallest is the min, the largest is the max

anonymous · Answer

oops typo there 
i meant of course check $f(-\frac{1}{2})$

anonymous · Answer

oh okay, i got it now.

anonymous · Answer

good!