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Airida [17]
1 year ago
8

How derivative of this absolute value function is like this!

Mathematics
1 answer:
Daniel [21]1 year ago
6 0

Recall the definition of absolute value.

|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}

When x,

|x| = x \implies \dfrac{d|x|}{dx} = 1

When x,

|x| = -x \implies \dfrac{d|x|}{dx} = -1

The derivative does not exist at x=0, since the one-sided limits

\displaystyle \lim_{x\to0^-} f'(x) = -1

and

\displaystyle \lim_{x\to0^+} f'(x) = +1

do not match.

So the derivative of |x| is

\dfrac{d|x|}{dx} = \begin{cases} 1 & \text{if } x > 0 \\ -1 & \text{if } x < 0 \\ \text{undefined} & \text{if } x = 0\end{cases}

Now we can write this as

\dfrac{d|x|}{dx} = \dfrac x{|x|} = \dfrac{|x|}x

since

x > 0 \implies |x| = x \implies \dfrac{|x|}x = \dfrac xx = 1

and

x < 0 \implies |x| = -x \implies \dfrac{|x|}x = -\dfrac xx = -1

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Step-by-step explanation:

Reflecting over y = -x maps (x, y) \longrightarrow (-y, -x).

So, F(1,-3) \longrightarrow F'(3, -1)

5 0
1 year ago
Внешний диаметр полого шара равен 16 см. Толщина стенок 2 см Найти
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Answer:

Внешний радиус

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8 0
3 years ago
Read 2 more answers
Find the value of x in the triangle shown below 5 3
Alika [10]

Answer: 4

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8 0
2 years ago
I need help with these two questions
BlackZzzverrR [31]
Problem 4

Answer: 47

------------------------

Work Shown:

f(x) = x^2 - 7x + 3
f(x) = (x)^2 - 7(x) + 3
f(-4) = (-4)^2 - 7(-4) + 3 ... replace each x with -4
f(-4) = 16 - 7(-4) + 3
f(-4) = 16 + 28 + 3
f(-4) = 44 + 3
f(-4) = 47

============================================================

Problem 5

Answer: See the attached image for the table

------------------------

Work Shown:

Plug in n = 27 and we get...
C = 26 + 10*n
C = 26 + 10*27
C = 26 + 270
C = 296
The input n = 27 leads to the output C = 296. This means that 27 people will have the cost be $296

Do the same for n = 39
C = 26 + 10*n
C = 26 + 10*39
C = 26 + 390
C = 416
The input n = 39 leads to the output C = 416. This means that 39 people will have the cost be $416

and also n = 43 as well
C = 26 + 10*n
C = 26 + 10*43
C = 26 + 430
C = 456
The input n = 43 leads to the output C = 456. This means that 43 people will have the cost be $456

4 0
3 years ago
QUESTION 1
lukranit [14]
1.) 2368000 (two million, three hundred sixty-eight thousand)
2.) 864,346,000 rounded to nearest thousand
3.) 864,345,537.00 not 100% on the last answer

Good luck
8 0
3 years ago
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