Write an equation involving absolute value or the graph

Answer:

[tex]\displaystyle b = -22[/tex]

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = (x^3+bx+6)(g(x))[/tex]

Where b is a constant and g is a differentiable function.

And we want to determine the value of b such that f'(2) = 0.

Find f' using the product rule:

[tex]\displaystyle \begin{aligned} f'(x) & = \frac{d}{dx}\left[ (x^3+bx+6)(g(x))\right] \\ \\ & = \frac{d}{dx}\left[ x^3 + bx + 6\right] g(x) + (x^3+bx+6)\frac{d}{dx}\left[ g(x)\right] \\ \\ & = (3x^2+b)(g(x)) + (x^3 + bx + 6)(g'(x))\end{aligned}[/tex]

Substitute using known values and solve for b:

[tex]\displaystyle \begin{aligned}f'(2) = 0 & = (3(2)^2+b)(g(2)) + ((2)^3+b(2)+6)(g'(2)) \\ \\ 0 & = (12+b)(3) + (14+2b)(-1) \\ \\ 0 & = 22 +b \\ \\ b & = -22\end{aligned}[/tex]

In conclusion, the value of b is -22.

The function f is given b is a constant and g is a differentiable function the value b (-8.4),

Let's start by finding the derivative of the given function f(x) with respect to x:

f(x) = (x³ + bx + 6) × g(x)

Using the product rule for differentiation, the derivative of f(x) is:

f'(x) = (x³ + bx + 6) × g'(x) + g(x) × (3x² + b)

Now we are interested in finding the value of b for which f'(2) = 0. So, let's plug in x = 2 and use the information given about g(2) and g'(2):

f'(2) = (2³ + 2b + 6) × g'(2) + g(2) × (3 × 2² + b)

Since g(2) = 3 and g'(2) = -1,

f'(2) = (8 + 2b + 6) × (-1) + 3 × (3 × 4 + b)

= (2b + 14 - 8) + 3× (12 + b)

= 2b + 6 + 36 + 3b

= 5b + 42

Now, we want to find the value of b for which f'(2) = 0:

5b + 42 = 0

Subtracting 42 from both sides:

5b = -42

Dividing both sides by 5:

b = -8.4

To know more about function here

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Complete question:

The function f is given by f(x)=(x^{3}+bx+6)(g(x)), where b is a constant and g is a differentiable function satisfying g(2)=3 and g′(2)=−1. For what value of b is f′(2)=0?

7

10

12

22

-8.4

Ignore this, I posted the wrong answer and I don't know how to delete it.

Answer:

Yes/true

Step-by-step explanation:

-2(z+9)-(-5)=-2⋅z-2⋅9+5

sostituisco la lettera dandogli un valore

=-2(-6+9)-(-5)=-2⋅(-6)-2⋅9+5

calcolo e tolgo le parentesi

=-2⋅3+5=12-18+5

Elimino i termini uguali

=-2⋅3=12-18

Somma e moltiplicazione tra i numeri

=-6=-6

Answer:

a. 125

Step-by-step explanation:

the angle labeled "x" is supplementary with the angle that has a measure of 55°

Supplementary angles add up to equal 180°

This means that x + 55 must equal 180

Note that we've just created an equation that we can use to solve for x.

We now solve for x using the equation we just created.

x + 55 = 180

subtract 55 from both sides

x = 125

The answer is a

Answer:

0.65 cents

Step-by-step explanation:

12x4=48 total

31.20/48 = 0.65 cents each

Answer:

  24

Step-by-step explanation:

Let d represent the number of dimes. Then (57-d) is the number of quarters, and the total value (in cents) is ...

  10d +25(57 -d) = 1065

  -15d +1425 = 1065 . . . . . . simplify

  -15d = -360 . . . . . . . . . . subtract 1425

  d = -360/-15 = 24 . . . divide by the coefficient of d

There are 24 dimes in the jar.

f we plot the provided points, we'd end up with something like the picture below, which is a line, mind you a declining line from left to right, so we can pretty see it has a negative slope, to get the slope we can just pick any two given points and check what it might be as well as get its equation, hmmm let's use the points of (4,-8) and (2,8)[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{4}}}\implies \cfrac{8+8}{-2}\implies \cfrac{16}{-2}\implies -8 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{-8}(x-\stackrel{x_1}{4})\implies y =-8x+24[/tex]

so is linear because it has a slope (common difference) of -8,

Use the property of similarity of triangles =》the corresponding sides of a triangle should be in the same ratio.

Take the missing side as 'x'.

The corresponding sides here are,

■ 7 & 14 ft

■ 5 & x ft

7/14 = 5/x

7x = 5 × 14 (cross multiplication)

7x = 70

x = 70/7

x = 10 ft

Height of the tree = 10 ft.

_____

Hope it helps ⚜

Answer:

1.9375

Step-by-step explanation:

used a clacalator

Answer:

31/16 or 1.9375 or 1 and 15/16

Step-by-step explanation:

Answer:

The side of an equilateral triangle equals:

2 * height / sqr root (3)

side = 2 * sqr root (12) / sqr root (3)

side = 2 * 2 * sqr root (3) / sqr root (3)

side x = 4

Step-by-step explanation:

Answer:

Use points (4,1) and (3,-1)

Step-by-step explanation:

Let's say the other coordinates are (x,y).

Then, we know (1-y)/(4-x)=2. So if y is -1, and x is 3, then we get:

[1-(-1)]/(4-3)=2/1=2

So draw the two points, (4,1) and (3,-1) on a coordinate plane, and use a ruler to make a line that goes through both the points.

Answer:

-6/5

Step-by-step explanation:

I hope it helps, bye

Answer:

1st= 2.4 on the line

2nd= -0.5 on the line

3rd=2.1 on the line

Step-by-step explanation:

1st=because each line represents 1 part so if it is split into 5 you have to treat 2 lines as one

2nd 1/2=0.5 so -1/2= -0.5

3rd if one line is one part then it is 2.1

Answer:

9/10

Step-by-step explanation: the magic mushroom said so

Answer:

(-2,5)

Step-by-step explanation:

Answer:

he can run 4.2 miles

Step-by-step explanation:

rate=distance/time

6 miles/50min =3/25 miles per min

rate=distance//time

3/25=distance/35

3/25 * 35 =distance

4.2 =distance

Answer:

b

Step-by-step explanation:

mark brainliest pls....

Answer:

The second one is the answer.

Step-by-step explanation:

slope= y2-y1

          ------------

            x2-x1

Answer:

18

Step-by-step explanation:

let the be x

if the middle sized pipe is 6 inches longer than the smallest.

so 24 subtract from 6=18

Answer:

1: x =(16-√392)/2=8-7√ 2 = -1.899

2: x =(16+√392)/2=8+7√ 2 = 17.899

Step-by-step explanation: I found two solutions it’s either one or two.

I hope this helped :) I tried my best.

Answer:

BDE

Step-by-step explanation:

Raise [tex]6[/tex] to the second power, [tex]6^{2}[/tex], the subtract r from the result, that should be [tex]6^{2} - r[/tex], since we are not to simplify the expression, that's the answer.

Answer: $3583.33

Step by Step Explanation:

43,000 * 1/12 = 43,000/12 = $3583.33

Answer:

7 miles / hour

Step-by-step explanation:

I'm taking this to mean she walked 3.5 miles. She did this 1/2 hour.

Givens

d (distance ) = 3.5 miles

t (time) = 1/2 hour

r (rate) = ?

Formula

r = d/t

Solution

The easiest way to do this is to change the fractions to decimals.

t = 1/2 = 0.5 hours

r = 3.5 / 0.5

r = 7 miles per hour.

Answer:

4/3 1.333 1 1/3

Step-by-step explanation:

Answer:

X = -1 (unsure as to how this is not an answer but I have checked my work)

Step-by-step explanation:

( f(x) = y )

1. y = 2x + 2

  -2         -2

2. -2 = 2x

    /2     /2

3. -1 = x

Answer:

7.9 pounds of fruit

Step-by-step explanation:

In all means to add, so 7 + .9 = 7.9 pounds

Answer:

it would need 40 liters of natural oil

8x5=40