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Find the maximum and minimum values of

0 votes

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

asked Mar 10, 2015 in PRECALCULUS by anonymous

2 Answers

0 votes

Step 1:

The function is .

Apply derivative with respect to image.

Sum rule of derivatives : .

image

image

image

Step 2:

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

image

image

for .

image

for .

is not in the region.

Critical points in the given interval are image.

So the test intervals are image, image and image.

answered Mar 12, 2015 by sandy Pupil
0 votes

contd.....

Step 3:

First derivative test:

Extremes :

If image on an open interval extending left from  image and

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

image

image

If image on an open interval extending left from image and

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

image

Solution :

Maximum  = image.

Minimum = image.

answered Mar 12, 2015 by sandy Pupil
edited Mar 12, 2015 by sandy

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