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anonymous

  • one year ago

Need help ASAP please! Two students in your class, Tucker and Karly, are disputing a function. Tucker says that for the function, between x = -3 and x = 3, the average rate of change is 0. Karly says that for the function, between x = -3 and x = 3, the graph goes up through a turning point, and then back down. Explain how Tucker and Karly can both be correct, using complete sentences.

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  1. anonymous
    • one year ago
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    @hartnn please help me :(

  2. anonymous
    • one year ago
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    @Miracrown I'll give medal, please help!

  3. anonymous
    • one year ago
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    @nincompoop

  4. anonymous
    • one year ago
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    @ganeshie8 please help me!!

  5. Rushwr
    • one year ago
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    @abb0t Please help ????

  6. Empty
    • one year ago
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    I think a picture could probably help |dw:1439623078585:dw| So this function's average height is about at y=0 and it has a turning point as well between x=-3 and x=3. There are other possible functions as well that could do this too such as a sine function for instance, even though I basically just made kinda like a parabola for the picture. So hopefully you can use this example to come up with your own answers?

  7. Rushwr
    • one year ago
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    Thank you @Empty

  8. arindameducationusc
    • one year ago
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    nice @Empty

  9. Empty
    • one year ago
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    To find the average height of a function over an interval, you sort of do something similar to taking the average of discrete things. Take the sum of the values over the total, but in calculus we turn these sums for the the values into an integral and the total is the interval: \[\text{avg} = \frac{\int_a^b f(x) dx}{b-a}\] So here the average height was 0, and I wanted to make a function that looks like what I have here, so I will use \(f(x)=-x^2+a\) and solve for \(a\). \[0 = \frac{1}{3-(-3)} \int_{-3}^3 -x^2+a dx\] We can simplify this a bit: \[0 = \int_0^3 -x^2 +a dx\] \[0 = -\frac{3^3}{3} + a3\] \[a=3\] So an example of a function that has a turning point on the interval [-3,3] and an average height of zero is \(f(x)=-x^2+3\). There are really infinitely many other functions that satisfy this situation though, this just happens to be a simple one to construct that meets our requirements here.

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