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Snezhnost [94]
3 years ago
15

Evaluate: 2|x-4|+6 for x=2

Mathematics
1 answer:
Lina20 [59]3 years ago
6 0
<h3>Answer:</h3>

10

<h3>Step-by-step explanation:</h3>

2|x -4| +6 \text{ for } x = 2 \\ 2|2 -4| +6 \\ 2|-2| +6 \\ 2(2) +6 \\ 4 +6 \\ 10

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Which property does this represent?
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10. Determine the open interval(s) on which the function f(x) = 12x - x^3 is increasing.
Gre4nikov [31]

Answer:

\large\boxed{x\in(-2,\ 2)}

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Calculate the zeros of the derivative:

f'(x)=0\Rightarrow12-3x^2=0\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2=12\qquad\text{divide both sides by 3}\\\\x^2=4\to x=\pm\sqrt4\\\\x=\pm2

Let's check the derivative sign:

f'(x)>0\iff12-3x^2>0\qquad\text{use the distributive property}\\\\-3(x^2-4)>0\\\\-3(x^2-2^2)>0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\-3(x-2)(x+2)>0\\^{\qquad x=2\qquad x=-2

Sketch a parabola open down

(before the brackets there is the number -3 < 0)

Look at the picture.

Where the derivative is negative, the function decreases.

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(p+2)(p-2)

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(p²+4)(p+2)(p-2)

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