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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?

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  1. dumbcow
    • 4 years ago
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    basically its the slope formula: f(3) -f(1)/ 3-1

  2. anonymous
    • 4 years ago
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    how did u get that?

  3. campbell_st
    • 4 years ago
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    find f(1) and f(3) average rate of change is \[m = [(f(3) - f(1)]/(3 - 1)\]

  4. dumbcow
    • 4 years ago
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    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
    • 4 years ago
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    so can i use m= Y2-Y1/X1-X2 ?

  6. dumbcow
    • 4 years ago
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    yep the avg slope in that interval is the same as the slope of the line connecting the 2 endpoints

  7. anonymous
    • 4 years ago
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    0/2 ?

  8. dumbcow
    • 4 years ago
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    ok yeah thats it. 0/2 = 0 so the avg slope is 0

  9. anonymous
    • 4 years ago
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    g(x)=mx+b, x1<x<x2

  10. anonymous
    • 4 years ago
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    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. dumbcow
    • 4 years ago
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    just plug it into the formula g(x2)-g(x1)/ x2-x1

  12. anonymous
    • 4 years ago
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    and then ?

  13. anonymous
    • 4 years ago
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    finish?

  14. dumbcow
    • 4 years ago
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    simplify, you should find that things cancel

  15. anonymous
    • 4 years ago
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    mX2-mX1/X2-X1 ?

  16. dumbcow
    • 4 years ago
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    yep, now factor out the m

  17. anonymous
    • 4 years ago
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    answer is m ?

  18. dumbcow
    • 4 years ago
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    yep :)

  19. anonymous
    • 4 years ago
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    If f(x)=1/3^x and g(x)=x^3, what is the domain of (f.g)(x)?

  20. anonymous
    • 4 years ago
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    (f into g)(x)

  21. anonymous
    • 4 years ago
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    {x E R} ?

  22. dumbcow
    • 4 years ago
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    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
    • 4 years ago
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    (f.g)(x) divided

  24. anonymous
    • 4 years ago
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    f(x).g(x)

  25. anonymous
    • 4 years ago
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    multiply

  26. dumbcow
    • 4 years ago
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    ??

  27. anonymous
    • 4 years ago
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    f(x) and g(x) are multiply

  28. dumbcow
    • 4 years ago
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    1/3^x * x^3

  29. anonymous
    • 4 years ago
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    yeah

  30. dumbcow
    • 4 years ago
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    thats it

  31. anonymous
    • 4 years ago
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    what is the domain?

  32. dumbcow
    • 4 years ago
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    oh, all real num there is no x value that makes it undefined

  33. anonymous
    • 4 years ago
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    {x E R} ? x is not equal -1 ?

  34. dumbcow
    • 4 years ago
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    umm well R is used as notation for the set of all real numbers

  35. anonymous
    • 4 years ago
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    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 } ?

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