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vodomira [7]
3 years ago
9

Which graph represents an increasing function? (1 point)

Mathematics
1 answer:
vladimir1956 [14]3 years ago
7 0

Answer:

graph b

Step-by-step explanation:

it's the only one that has a positive slope

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How do I differentiate this?​
disa [49]

Answer:

\frac{8}{\left(-x+2\right)^2} & x = 1, x = 3

Step-by-step explanation:

I'm sure you are familiar with the product rule,

If y = u*v => dy/dx = u * dv/dx + v * dy/dx <----- product rule

In this case:

u=3x+2,\:v=\left(2-x\right)^{-1},\\=>\frac{d}{dx}\left(3x+2\right)\left(2-x\right)^{-1}+\frac{d}{dx}\left(\left(2-x\right)^{-1}\right)\left(3x+2\right)

Now remember the sum rule:

\frac{d}{dx}\left(3x+2\right) = \frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(2\right),\\\frac{d}{dx}\left(3x\right) = 3,\\\frac{d}{dx}\left(2\right)  = 0\\\frac{d}{dx}\left(3x+2\right) = 3

For this second bit we apply the chain rule:

\frac{d}{dx}\left(\left(2-x\right)^{-1}\right) = -\frac{1}{\left(2-x\right)^2}\frac{d}{dx}\left(2-x\right),\\\frac{d}{dx}\left(2-x\right) = -1,\\\\=> -\frac{1}{\left(2-x\right)^2}\left(-1\right)\\=> \frac{1}{\left(2-x\right)^2}

If we substitute these values back into the expression...\frac{d}{dx}\left(3x+2\right)\left(2-x\right)^{-1}+\frac{d}{dx}\left(\left(2-x\right)^{-1}\right)\left(3x+2\right)

...we get the following:

3\left(2-x\right)^{-1}+\frac{1}{\left(2-x\right)^2}\left(3x+2\right)

The rest is just pure simplification:

3\left(2-x\right)^{-1}+\frac{1}{\left(2-x\right)^2}\left(3x+2\right)\\= \frac{3}{-x+2}+\frac{3x+2}{\left(-x+2\right)^2}\\= \frac{3\left(-x+2\right)}{\left(-x+2\right)^2}+\frac{3x+2}{\left(-x+2\right)^2}\\\\= \frac{3\left(-x+2\right)+3x+2}{\left(-x+2\right)^2}\\\\= \frac{8}{\left(-x+2\right)^2}

Now let's equate this to equal 8 for the second bit and solve for x:

\frac{8}{\left(-x+2\right)^2}=8,\\\frac{8}{\left(-x+2\right)^2}\left(-x+2\right)^2=8\left(-x+2\right)^2,\\8=8\left(-x+2\right)^2,\\\left(-x+2\right)^2=1,\\x = 1, x = 3

4 0
3 years ago
Select all of the choices that are equal to (-5) - (-12)<br><br> -7<br> 7<br> (-5)+12<br> (-5)+(-12)
Roman55 [17]

Answer:

the awnser is. (-5) + (-12)

7 0
2 years ago
Read 2 more answers
Which relation is not a function?<br><br><br><br><br> Helppppo due now
IRISSAK [1]

Answer:

B.

Step-by-step explanation:

there cannot be two of the same x value's. It would make it a circle on the graph, or something close to that, which isn't a function.

5 0
2 years ago
The graph of F(x) can be flipped over a certain line to produce the graph of its inverse. What is the equation of that line?
OlgaM077 [116]
<span><u><em>The correct answer is: </em></u>
y=x.

<u><em>Explanation: </em></u>
<span>In order to find the inverse of a function, we first <u>switch x and y</u>; then we isolate y. When we do this, we are saying that x and y equal the same thing, or y=x.  </span></span>
4 0
3 years ago
Read 2 more answers
Which of the following numbers is not written in scientific notation?
Sonja [21]

Answer A

Step-by-step explanation:

Because there is a zero at the begining.

8 0
2 years ago
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