Find the largest and smallest values of the given function over the prescribed closed, bounded interval.
f(x)=x+1ln(x+1) for 0 ? x ? 2
f′(x)=(x+1)2x+11(1)(x+1)−(1)(ln(x+1))
f′(x)=(x+1)2x+1x+1−ln(x+1)
f′(x)=(x+1)21−ln(x+1)
0=(x+1)21−ln(x+1)
0=1−ln(x+1)
ln(x+1)=1
...don't know what to do now.
(x+1)2=0
(x+1)(x−1)=0
x=1, x=−1
f(0)=0
f(2)=0.3662
f(1)=0.34657
f(−1)=error
f(x)=x+1ln(x+1) for 0 ? x ? 2
f′(x)=(x+1)2x+11(1)(x+1)−(1)(ln(x+1))
f′(x)=(x+1)2x+1x+1−ln(x+1)
f′(x)=(x+1)21−ln(x+1)
0=(x+1)21−ln(x+1)
0=1−ln(x+1)
ln(x+1)=1
...don't know what to do now.
(x+1)2=0
(x+1)(x−1)=0
x=1, x=−1
f(0)=0
f(2)=0.3662
f(1)=0.34657
f(−1)=error