Question

Using analytical method, find the extreme values of the functions on the interval and where they occur.

1. f(x) = ln(x+1), 0<=x<=3

2. f(x) = sin(x+ pi/4), 0<=x<=(7pi)/4

Thanks in advance.

Answer 1

1. d/dx ln (x+1)+d/dx(x+1)
*remember to use the chain rule
=1/x+1 + 1

endpoints: plug in the numbers of the interval
f(0)=ln1=0
f(3)=ln(3+1)=ln4=1.386

maximum:ln4 at x=3
minimum:0 at x=0