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sp2606 [1]
3 years ago
11

The graph of the function f(x)=(x-4)(x+1) is shown below. which statement about the function is true?

Mathematics
1 answer:
Andrei [34K]3 years ago
3 0

Answer:

(3) the function is decreasing for all real numbers of x where x< 1.5

Step-by-step explanation:

The function given in this problem is

f(x)=(x-4)(x+1)

which can be rewritten as:

f(x)=x^2-4x+x-4=x^2-3x-4

A function is:

- Increasing over a certain interval if the first derivative f'(x) is positive in that interval

- Decreasing over a certain interval is the first derivative f'(x) is negative in that interval

So we start by calculating the first derivative of this function. We get:

f'(x)=2x^{2-1}-3x^{1-1}=2x-3

This function is positive when:

2x-3>0\\2x>3\\x>\frac{3}{2}

Which means, when x > 1.5.

So the function is:

- Increasing for x > 1.5

- Decreasing for x < 1.5

So the correct option is

(3) the function is decreasing for all real numbers of x where x< 1.5

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7 0
3 years ago
Read 2 more answers
Dada la sucesión an = 1700 + 4,1· n2 + 304,9· n
shutvik [7]

Concluimos que la opción correcta es <em>"Solo II"</em>.

Una expresión es una sucesión aritmética si y solo si existe entre dos elementos <em>consecutivos</em> cualesquiera de la serie la misma diferencia. La sucesión aritmética es definida por una expresión de la forma:

a_{n} = a + b\cdot n, n\in \mathbb{N} (1)

Donde a,b son coeficientes de la sucesión.

Asimismo, una expresión es una sucesión geométrica si y solo si entre dos elementos <em>consecutivos</em> cualesquiera de la serie existe la misma razón. La sucesión geométrica es definida por una expresión de la forma:

a_{n} = a\cdot r^{b\cdot n}, n\in \mathbb{N} (2)

Donde a, b, r son coeficientes de la sucesión.

Por último, una expresión es una sucesión monótona creciente si dados dos elementos <em>consecutivos</em> de una serie, el elemento posterior es siempre mayor que el elemento anterior. Matemáticamente, debe satisfacerse la siguiente condición:

\frac{a_{n+1}}{a_{n}} > 1, n\in \mathbb{N} (3)

Esta claro por inspección directa que la sucesión dada no es aritmética ni geométrica y cabe comprobar si es monótona creciente. Valiéndonos de (3), realizamos las operaciones algebraicas pertinentes:

r = \frac{1700 + 4,1\cdot (n+1)^{2}+304,9\cdot (n+1)}{1700 + 4,1\cdot n^{2}+304,9\cdot n}

r = \frac{1700+4,1\cdot (n^{2}+2\cdot n +1) +304,9\cdot (n+1)}{1700 + 4.1\cdot n^{2}+304,9\cdot n}

r = \frac{1700+4,1\cdot n^{2}+304,9\cdot n+4,1\dot (2\cdot n +1) +304.9}{1700+4,1\cdot n^{2}+304,9\cdot n}

r = 1 + \frac{8,2\cdot n +309}{1700 + 4,1\cdot n^{2}+304,9\cdot n}

Como puede apreciarse, r > 1. Por tanto, la sucesión es monótona y creciente.

En consecuencia, concluimos que la opción correcta es <em>"Solo II"</em>.

Invitamos cordialmente a leer esta pregunta sobre sucesiones: brainly.com/question/21709418

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Answer:

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Norm has $15,000 to deposit. His daughter is a junior in high school and plans to go to college. Recommend the best way for Norm
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Step-by-step explanation:

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2,4,6,8

I hope it is right

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