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Math Help - Im not sure if i understand this problem :(

  1. #1
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    Im not sure if i understand this problem :(

    Let f(x)=8x^2. Find a value A such that the average rate of change of f(x) from 1 to A equals 96.

    someone help me please
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  2. #2
    Nox
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    Hello.

    The rate of change from a to b is equal to:

    \frac{f(b)-f(a)}{b-a}

    So in your problem, you'd set 96 equal to that. What are a and b in your problem? For that matter, what are f(a) and f(b)?
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  3. #3
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    Quote Originally Posted by Nox View Post
    Hello.

    The rate of change from a to b is equal to:

    \frac{f(b)-f(a)}{b-a}

    So in your problem, you'd set 96 equal to that. What are a and b in your problem? For that matter, what are f(a) and f(b)?
    Im guessing A equals 1 and B is what I have to find.
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  4. #4
    Nox
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    Well, yes. And you may not know exactly what number A is, but you know that it's called "A," so you can use it in the equation. So what are f(1) and f(A)?
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  5. #5
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    Quote Originally Posted by Nox View Post
    Well, yes. And you may not know exactly what number A is, but you know that it's called "A," so you can use it in the equation. So what are f(1) and f(A)?
    i think f(1)=64 and f(a)=64A
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  6. #6
    Nox
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    Not quite. What you've done is f(x) = 8^2(x) instead of f(x) = 8(x)^2.

    In other words, square the value of the input and multiply that by 8. Don't square 8 and multiply it by the input, as you have done above.
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  7. #7
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    Quote Originally Posted by Nox View Post
    Not quite. What you've done is f(x) = 8^2(x) instead of f(x) = 8(x)^2.

    In other words, square the value of the input and multiply that by 8. Don't square 8 and multiply it by the input, as you have done above.
    so that means f(1)=8? i dont understand
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  8. #8
    Nox
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    Yup! f(1) = 8. Keep going!
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  9. #9
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    Quote Originally Posted by Nox View Post
    Yup! f(1) = 8. Keep going!
    okay....so f(1)=8
    which means f(A)=8A^2?
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  10. #10
    Nox
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    Also true. So put those two things back into the equation for rate of change (Remember! Order is important here.) and see what you get.
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  11. #11
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    Quote Originally Posted by Nox View Post
    Also true. So put those two things back into the equation for rate of change (Remember! Order is important here.) and see what you get.
    f(b)-f(a) / b-a
    f(b)-8A^2 / b-1

    where does the f(1) come into play? i feel slow
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  12. #12
    Nox
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    It's okay, don't feel bad. But b is A, and a is 1. f(b) - f(a) means f(A) - f(1)... in this case, 8A^2 - 8. Put that over b - a. (Which is, in this problem... ??) You're almost there!
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  13. #13
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    Quote Originally Posted by Nox View Post
    It's okay, don't feel bad. But b is A, and a is 1. f(b) - f(a) means f(A) - f(1)... in this case, 8A^2 - 8. Put that over b - a. (Which is, in this problem... ??) You're almost there!
    8A^2-8/A-1?
    And then do I set that to 96?
    8A^2-8/A-1=96
    And i think you multiply both sides by A-1
    8A^2-8=96A-96
    Is this right so far?
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  14. #14
    Nox
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    Yes! Good work so far, keep going.
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  15. #15
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    wow....im stuck. can someone help me?

    btw nox, thank you very very much for your help...i appreciate it
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