## anonymous 4 years ago What is the average rate of change of the function f(x)= X^2-4x+7 on the interval 1<x<3?

1. anonymous

basically its the slope formula: f(3) -f(1)/ 3-1

2. anonymous

how did u get that?

3. campbell_st

find f(1) and f(3) average rate of change is $m = [(f(3) - f(1)]/(3 - 1)$

4. anonymous

rate of change = slope technically avg rate of change is defined as: $\frac{1}{b-a}\int\limits_{a}^{b} f'(x) dx = \frac{f(b) -f(a)}{b-a}$

5. anonymous

so can i use m= Y2-Y1/X1-X2 ?

6. anonymous

yep the avg slope in that interval is the same as the slope of the line connecting the 2 endpoints

7. anonymous

0/2 ?

8. anonymous

ok yeah thats it. 0/2 = 0 so the avg slope is 0

9. anonymous

g(x)=mx+b, x1<x<x2

10. anonymous

Without doing any calculation, how can one determine the average rote of change of g(x)= mx+b over the interval X1<X<X2 ?

11. anonymous

just plug it into the formula g(x2)-g(x1)/ x2-x1

12. anonymous

and then ?

13. anonymous

finish?

14. anonymous

simplify, you should find that things cancel

15. anonymous

mX2-mX1/X2-X1 ?

16. anonymous

yep, now factor out the m

17. anonymous

18. anonymous

yep :)

19. anonymous

If f(x)=1/3^x and g(x)=x^3, what is the domain of (f.g)(x)?

20. anonymous

(f into g)(x)

21. anonymous

{x E R} ?

22. anonymous

so you are plugging g(x) into the variable for f --> 1/3^g(x) = 1/3^(x^3) domain is all possible x_values

23. anonymous

(f.g)(x) divided

24. anonymous

f(x).g(x)

25. anonymous

multiply

26. anonymous

??

27. anonymous

f(x) and g(x) are multiply

28. anonymous

1/3^x * x^3

29. anonymous

yeah

30. anonymous

thats it

31. anonymous

what is the domain?

32. anonymous

oh, all real num there is no x value that makes it undefined

33. anonymous

{x E R} ? x is not equal -1 ?

34. anonymous

umm well R is used as notation for the set of all real numbers

35. anonymous

i mean x can't be equal -1 or x can't be equal 0 or x can't be equal 1 or just { x E R } ?