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adell [148]
3 years ago
12

Given the following polynomial find the maximum possible number of turning points. f(x)=x^11+x^10+x^12+x^9

Mathematics
1 answer:
11111nata11111 [884]3 years ago
5 0
Turning points are inflection points

think
1st degree (linear) has no turning/inflecion points
2nd degree (quadratic, parabola) has  1 turning/inflection point
so
nth degree has n-1 turning/inflection point

this is 11th degree since highest power is 12
12-1=11
11 turning oints
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Step-by-step explanation:

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2\frac{7}{21}+\frac{9}{21} / 2\frac{7}{21} * 1\frac{9}{21}

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2\frac{16}{21} / 2\frac{7}{21} * 1\frac{9}{21}

3. We can do the same thing to the other side, by multiplying the two of them. I'm going to convert both of them to just fractions, 2\frac{7}{21} becomes \frac{49}{21} and 1\frac{9}{21} becomes \frac{30}{21}

\frac{49}{21} *  \frac{30}{21}

Now we can reduce them, and for our first fraction divide the top and bottom by 7, giving us  \frac{7}{3} and the second one by 3, which gives us  \frac{10}{7}

\frac{7}{3} * \frac{10}{7} now we cross divide, where we replace the 7's with ones because they're right across from each other to get  \frac{1}{3} and  \frac{10}{1}, or just 10.

\frac{1}{3} * 10 =  \frac{10}{3}

4. So now we can do a similar thing with the first half of our equation and convert it into a fraction and not a mixed number.

\frac{58}{21} / \frac{10}{3}

Now we multiply divide them, and the easiest way I learned how to do this was by keep the first fraction in its place, and flipping the denominator and numerator of the second, and multiplying them.

so   \frac{58}{21} * \frac{3}{10} which if we multiply both sides, you get \frac{174}{210}

I'll save you some times and simplify it for you, the greatest common factor is 6 so we divide the top and bottom by 6 to get

\frac{29}{35}

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