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VikaD [51]
3 years ago
8

Is the function increasing or decreasing over the interval (-3,-1)? Explain.

Mathematics
2 answers:
rusak2 [61]3 years ago
7 0
Increasing it is going up
Tatiana [17]3 years ago
4 0
<h3>Answer: Decreasing</h3>

Explanation:

The curve is going downhill as you move from left to right, and as you move from x = -3 to x = -1.

The interval notation of (-3,-1) means -3 < x < -1.

Since the curve is going downhill on this region, this means the function is decreasing on this interval.

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x = -2

Step-by-step explanation:

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3 years ago
<img src="https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B%20%20%5Csqrt%7B3x%7D%20%7D%7B1%20%2B%20e%5E%7B2x%7D%20%7D%20" id="TexF
kumpel [21]

~~~~~~~~y = \dfrac{\sqrt{3x}}{ 1+ e^{2x}}\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx}  \left( \dfrac{\sqrt{3x}}{1+ e^{2x}} \right)\\\\\\~~~~~~~~~~~~=\dfrac{(1 + e^{2x} ) \dfrac{d}{dx} \left(\sqrt{3x} \right) - \left(\sqrt{3x} \right)\dfrac{d}{dx}(1+e^{2x})}{\left( 1+ e^{2x} \right)^2}~~~~~~~~~~~~;[\text{Quotient rule}]\\\\\\~~~~~~~~~~~~=\dfrac{(1+e^{2x}) \cdot \dfrac{1}{2\sqrt{3x}} \cdot 3-\left(\sqrt{3x} \right) \cdot 2 e^{2x}}{(1 + e^{2x})^2}~~~~~~~~~~~~~~~~~~~~;[\text{Chain rule}]\\\\\\

            =\dfrac{\dfrac{\sqrt 3 (1 + e^{2x})}{2\sqrt x} -2e^{2x} \sqrt{3x}}{(1+e^{2x})^2}\\\\\\=\dfrac{\tfrac{\sqrt 3(1 +e^{2x}) - 4x\sqrt 3 e^{2x}}{2\sqrt x}}{(1+e^{2x})^2}\\\\\\=\dfrac{\sqrt 3(1+e^{2x} -4xe^{2x})}{2\sqrt x(1 +e^{2x})^2}

7 0
2 years ago
What is the standard deviation of the population: Use the stdevp function in the Desmos graphing calculator.
Mice21 [21]

The standard deviation of the given data is 3.5

<h3 /><h3>How to calculate the standard deviation of data?</h3>

Standard deviation is used to determine the rate of dispersion of data with respect to the mean.

The formula for calculating the standard deviation of data is given as:

\sigma = \sqrt{\frac{\sum (x-\overline x)^2}{n-1} }

Given the data below:

10.4, 10.3, 11.7, 11.1, 8, 4.4, 2.6, 1.8, 2.5, 4.4, 7.3, 9.5

Using the stdevp calculator the standard deviation is calculated as:

σ =  √12.405

σ = 3.5

Hence the standard deviation of the given data is 3.5

Learn more on standard deviation here: brainly.com/question/12402189

8 0
2 years ago
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