Find the maximum and minimum values of

Question

 y = θ + 2 sin(θ) on the interval [0, 2π].?

Answer 1

Step 1:

The function is .

Apply derivative with respect to .

Sum rule of derivatives : .

Step 2:

To find the critical numbers of y, equate to zero.

for .

for .

is not in the region.

Critical points in the given interval are .

So the test intervals are , and .

Answer 2

contd.....

Step 3:

First derivative test:

Extremes :

If on an open interval extending left from  and

on an open interval extending right from  , then y has a relative maximum at .

If on an open interval extending left from and

on an open interval extending right from , then f has a relative minimum at .

Solution :

Maximum  = .

Minimum = .