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

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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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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