# Finding Critical Numbers; Finding the Extrema in the Interval; etc.

1. Find all the critical numbers: .

2. Find all the extrema in the interval [0,2 ] for .

3. Find the absolute maximum and the absolute minimum on the interval (1,4].

4. State why Rolle's Theorem does not apply to the function on the interval [-2,0].

5. Find all relative extrema of , include the designation of maximum or minimum.

6. Find all the points of inflection of the graph of the function .

7. Find the horizontal asymptote(s) for .

8. Find the limit: .

9. Find two numbers whose product is maximum if the sum of the first number and five times the second is 80.

10. Calculate 3 iterations of Newton's Method to approximate the real zero of .

https://brainmass.com/math/calculus-and-analysis/critical-numbers-extrema-interval-23111

#### Solution Preview

Hello and thank you for posting your question to Brainmass!

Please see the attachments to find your solution.

Find all the critical numbers:

Solution: x=-3

> y:=(x-1)/(x+3);

>

> CriticalPoints(y,x);

Find all the extrema in the interval [0,2 ] for .

Solution:

Find the absolute maximum and the absolute minimum on the interval (1,4].

Note that

Minima: (3,-3)

Maxima: (1,1)

State why ...

#### Solution Summary

The solution is attached in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you. The solution is given in great detail, graphs and equations all included.