Question

use analytic methods to find the extreme values of h(x)= ln(x+1) on the interval 0≤x≤3

Answer 1

First check the endpoints:
\[f(0)=\ln(0+1)=0\\
f(3)=\ln(3+1)=\ln4\]
Now use the derivative test:
\[f'(x)=\frac{1}{x+1}\]
The derivative is never zero, and over the interval \(0\le x\le3\), the value of the derivative is decreasing. What can you say about the extreme values?