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Expert: - 3/14/2008


Question
hi

how can i find the graph & the equation for these two statements:

- An odd-degree function with 3 relative maximum, 3 relative minimum and negative end behavior on the right.


- An even-degree function with 4 relative maximum, 3 relative minimum.


Answer
Odd degree means all of the exponets are odd.  If there is one max/min, the order on x is 1+1.  If there are two max/min, the order on x is 2+1.  We need 3+3=6, so the order is 6+1.  You might need the first 7=3+3+1 odd numbers as power on x to get 3 maximum and 3 minimum.  Note the behaviour on the right is determined by the highest power.

For even degree polynomials, it looks like you need the first 4+3+1=8 even exponents on x.

Note that the polynomial generated by (x-2)(x+2) has two roots and only even powers of x.  Multiply by x to get an odd degree polynomial.

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