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3 years ago

10

Suppose h” is continuous at x = 2,h' (2) = 0, and h” (2) < 0.

1 answer:

Katarina [22]3 years ago

7 0

Answer:

Hello,

Step-by-step explanation:

h(x) has a minimum at x= 2. (h(x) is turning down at x=2)

I have suppose that h''(2 + ) <0 and h''(2 -) <0

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Find the polynomial of minimum degree, with real coefficients, zeros at x=4±2⋅i and x=−8, and y-intercept at −480. Write your an

valkas [14]

Answer:

The polynomial of minimum degree is $p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$ .

Step-by-step explanation:

According to the statement, we appreciate that polynomial pass through the following points:

(i) $(4 + 2\,i,0)$ , (ii) $(4 - 2\,i, 0)$ , (iii) $(-8, 0)$ , (iv) $(0, -480)$

From Algebra we know that any n-th grade polynomial can be constructed by knowing n+1 different points. Hence, the polynomial of minimum degree is a quartic function. The polynomial has the following form:

$p(x) = (x-4-2\,i)\cdot (x-4+2\,i)\cdot (x+8)\cdot (x-r_{1})$

We proceed to expand the expression until standard form is obtained:

$p(x) = (x^{2}-4\cdot x-2\,i\cdot x-4\cdot x +16+8\,i+2\,i\cdot x-8\,i+4)\cdot (x+8)\cdot (x-r_{1})$

$p(x) = (x^{2}-8\cdot x+20)\cdot (x+8)\cdot (x-r_{1})$

$p(x) = (x^{3}-8\cdot x^{2}+20\cdot x +8\cdot x^{2}-64\cdot x+160)\cdot (x-r_{1})$

$p(x) = (x^{3}-44\cdot x +160)\cdot (x-r_{1})$

If we know that $p (0) = -480$ , then:

$-480=160\cdot (-r_{1})$

$-160\cdot r_{1} = -480$

$r_{1} = 3$

Then, the polynomial is:

$p(x) = (x^{3}-44\cdot x +160)\cdot (x-3)$

$p(x) = x^{4}-44\cdot x^{2}+160\cdot x-3\cdot x^{3}+132\cdot x -480$

$p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$

The polynomial of minimum degree is $p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$ .

5 0

3 years ago

enot [183]

Answer:

b

Step-by-step explanation:

...

4 0

2 years ago

Write a proof. Given x = 2 = 3 (x - 4) Prove x = 5

Galina-37 [17]

Step-by-step explanation:

The equation in the question is false.

$x - 2 = 3(x - 4)$

$x - 2 = 3x - 12$

$3x - x = 12 - 2$

$2x = 10$

$x = 10 \div 2$

$x = 5$

6 0

3 years ago

Can someone help me with this? I literally cant think today. ;-; Thanks if you answer it correctly. ಥ‿ಥ

AleksandrR [38]

Answer:

The slope is 300

Step-by-step explanation:

Rise over run we see two points how many times do we rise and run to get there?

(Slope= rise/run)

So you rise 300 times (Since half of 600 is 300) then you run 1 time which is 300/1 which is 300

4 0

3 years ago

25 points.<br> View attachment below.

Veseljchak [2.6K]

Answer:

d

Step-by-step explanation:

6 0

3 years ago

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