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3 years ago

What is the maximum number of relative extrema a polynomial function can have?

1 answer:

4 0

Relative extrema occur where the derivative is zero (at least for your polynomial function). So taking the derivative we get

20x3−3x2+6=0

 This is a 3rd degree equation, now if we are working with complex numbers this equation is guaranteed to have 3 solutions by the fundamental theorem of algebra. But the number of real roots are 1 which can be found out by using Descartes' rule of signs. So the maximum number of relative extrema are 1.

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VEEL

Andre45 [30]

Answer:

$a_n=-3(3)^{n-1}$ ; {-3,-9, -27,- 81, -243, ...}

$a_n=-3(-3)^{n-1}$ ; {-3, 9,-27, 81, -243, ...}

$a_n=3(\frac{1}{2})^{n-1}$ ; {3, 1.5, 0.75, 0.375, 0.1875, ...}

$a_n=243(\frac{1}{3})^{n-1}$ ; {243, 81, 27, 9, 3, ...}

Step-by-step explanation:

The first explicit equation is

$a_n=-3(3)^{n-1}$

At n=1,

$a_1=-3(3)^{1-1}=-3$

At n=2,

$a_2=-3(3)^{2-1}=-9$

At n=3,

$a_3=-3(3)^{3-1}=-27$

Therefore, the geometric sequence is {-3,-9, -27,- 81, -243, ...}.

The second explicit equation is

$a_n=-3(-3)^{n-1}$

At n=1,

$a_1=-3(-3)^{1-1}=-3$

At n=2,

$a_2=-3(-3)^{2-1}=9$

At n=3,

$a_3=-3(-3)^{3-1}=-27$

Therefore, the geometric sequence is {-3, 9,-27, 81, -243, ...}.

The third explicit equation is

$a_n=3(\frac{1}{2})^{n-1}$

At n=1,

$a_1=3(\frac{1}{2})^{1-1}=3$

At n=2,

$a_2=3(\frac{1}{2})^{2-1}=1.5$

At n=3,

$a_3=3(\frac{1}{2})^{3-1}=0.75$

Therefore, the geometric sequence is {3, 1.5, 0.75, 0.375, 0.1875, ...}.

The fourth explicit equation is

$a_n=243(\frac{1}{3})^{n-1}$

At n=1,

$a_1=243(\frac{1}{3})^{1-1}=243$

At n=2,

$a_2=243(\frac{1}{3})^{2-1}=81$

At n=3,

$a_3=243(\frac{1}{3})^{3-1}=27$

Therefore, the geometric sequence is {243, 81, 27, 9, 3, ...}.

6 0

3 years ago

Can anyone plz help me asap with Part B and C.?

creativ13 [48]

Answer:

Please post a clearer screenshot...

Step-by-step explanation:

5 0

2 years ago

Convert 10009 out of 17%

Anvisha [2.4K]

Answer:

Step-by-step explanation:

To convert 10,009 to 17%, turn 17% to decimal and multiply that by 10,009 (10,009 * 0.17), which equals 1,701.53

IF you meant to convert the fraction 10,009/17% (read as "10,009 out of 17 percent, ") then simply convert 17% to a decimal (0.17) and divide 10,009 by 0.17 (10,009/0.17) which is about 58,876.47, for full decimal, use a calculator and do 10,009/0.17

The question is kind of confusing so tell me what you meant

6 0

2 years ago

3.) Solve by Elimination: 3x + y = 15 2x + y = 11

Travka [436]

Answer:

X = 4

Y = 3

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

meyer has 0.64 GB of space remaining on his ipod.he wants to download a pedometer app (0.24 GB), a photo app (0.403 GB), and a m

Wewaii [24]

He can either download both the pedometer and the math apps,
or he can download only the photo app and no more.

Pedometer + math = 0.54 GB. Fits in 0.64 GB.

Photo = 0.403 GB. Fits in 0.64 GB, but only 0.237 GB left.
Not enough for pedometer (0.24)
or math (0.3) .

3 0

2 years ago

Read 2 more answers