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    Finding Critical Numbers; Finding the Extrema in the Interval; etc.

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    1. Find all the critical numbers: .
    2. Find all the extrema in the interval [0,2 ] for .
    3. Find the absolute maximum and the absolute minimum on the interval (1,4].
    4. State why Rolle's Theorem does not apply to the function on the interval [-2,0].
    5. Find all relative extrema of , include the designation of maximum or minimum.
    6. Find all the points of inflection of the graph of the function .
    7. Find the horizontal asymptote(s) for .
    8. Find the limit: .
    9. Find two numbers whose product is maximum if the sum of the first number and five times the second is 80.
    10. Calculate 3 iterations of Newton's Method to approximate the real zero of .

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    https://brainmass.com/math/calculus-and-analysis/critical-numbers-extrema-interval-23111

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    Find all the critical numbers:

    Solution: x=-3

    > y:=(x-1)/(x+3);

    >
    > CriticalPoints(y,x);

    Find all the extrema in the interval [0,2 ] for .

    Solution:

    Find the absolute maximum and the absolute minimum on the interval (1,4].
    Note that

    Minima: (3,-3)
    Maxima: (1,1)

    State why ...

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