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Thread: Average rate of change on the inteval

  1. #1
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    Average rate of change on the inteval

    Hello, I've managed to solve (at least I think) the following problem:

    Find the average rate of change of f(x) = 2x2 -x + 1 on the interval [3, 3+h].

    Though I solved it in 2 different ways and ended up with 2 different answers. My answers were -7 or -11 + 2h. I'm not sure which is the right answer or if neither is right. I'm positive I managed to set up the formula correctly, which I showed below:

    F(x) = (2(3+h)2 - (3+h) + 1 - 16)/3+h-3

    Any help is appreciated, and if you provide an explanation I would be even more thankful.
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  2. #2
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    Re: Average rate of change on the inteval

    $\dfrac{f(3+h) - f(3)}{(3+h)-3}$

    $\dfrac{2(3+h)^2 - (3+h) + 1 - [2(3)^2 - 3 + 1]}{h}$

    $\dfrac{2(9+6h+h^2) - 3 - h + 1 - 16}{h}$

    $\dfrac{18 + 12h + 2h^2 - 3 - h + 1 - 16}{h}$

    now ... combine like terms in the numerator & finish it.

    you should get $11 + 2h$
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  3. #3
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    Re: Average rate of change on the inteval

    Quote Originally Posted by reina View Post
    Hello, I've managed to solve (at least I think) the following problem:

    Find the average rate of change of f(x) = 2x2 -x + 1 on the interval [3, 3+h].

    Though I solved it in 2 different ways and ended up with 2 different answers. My answers were -7 or -11 + 2h. I'm not sure which is the right answer or if neither is right. I'm positive I managed to set up the formula correctly, which I showed below:

    F(x) = (2(3+h)2 - (3+h) + 1 - 16)/3+h-3

    Any help is appreciated, and if you provide an explanation I would be even more thankful.
    It's good that you showed where you started, but it does not help us figure out where you went wrong in the working.

    Except for a missing pair of parentheses in the denominator of the difference quotient, your set up was correct.
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  4. #4
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    Re: Average rate of change on the inteval

    You say "I solved it in 2 different ways and ended up with 2 different answers". What were those two different ways?
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