I know there are a lot of question but they go hand in hand with this function..
ID: 3341770 • Letter: I
Question
I know there are a lot of question but they go hand in hand with this function......I've awarded points accordingly. Please take the time to give detail responses.
Consider the function f, where f(x) = x ln x
Sketch the graph of f by ansering and considering the following (where they exist):
1. What is the domain of f?
2. x-intercepts, ie zeros of f ?
3. y-intercepts, ie f(0) ?
4. Horizontal asymptotes ?
5. Vertical asymptotes ?
6. Even or odd symmetry?
7. Critical numbers of f, ie zeros of f ' ?
8. Extreme values of f ?
9. Regions in domain where f is increasing / decreasing ?
10. How are horizontal / vertical asymptotes approached?
11. Critical numbers of f ' , ie zeros of f '' ?
12. Inflection points ?
13. Regions in domain where f is concave up / concave down (specify) ?
14. Sketch the graph ?
15. Does f have an inverse? Why?
16. If not, find the interval of maximum continuous extent (length) over which an inverse of f can be defined ?
17. Find the formula for f (inverse) if feasible and / or the graph of f (inverse) ?
18. List any evident (or celebrity) values of f and f (inverse) ?
19. Denoting f (inverse) by g, what is the domain of g?
20. Find g ' (e). ?
21. Find g ' (Ne^N) ?
22. Denoting f ' by h, does f (inverse ) have an increase?
23. What is the domain of h?
24. Find the formula for h (inverse) if feasible and/or the graph of h (inverse) ?
25. What is the domain of h (inverse) ?
26. List any evident (or celebrity) values of h and h (inverse) ?
27. Is the inverse of the derivative of f the same as the derivative of the inverse of f ? why?
Explanation / Answer
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