Simplify the linear expression.

F(x) = 3x + x3

____ [38]

Answer:

Please check the explanation.

Step-by-step explanation:

Given

f(x) = 3x + x³

Taking differentiate

$\frac{d}{dx}\left(3x+x^3\right)$

$\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'$

$=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)$

solving

$\frac{d}{dx}\left(3x\right)$

$\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'$

$=3\frac{d}{dx}\left(x\right)$

$\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1$

$=3\cdot \:1$

$=3$

now solving

$\frac{d}{dx}\left(x^3\right)$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}$

$=3x^{3-1}$

$=3x^2$

Thus, the expression becomes

$\frac{d}{dx}\left(3x+x^3\right)=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)$

$=3+3x^2$

Thus,

f'(x) = 3 + 3x²

Given that f'(x) = 15

substituting the value f'(x) = 15 in f'(x) = 3 + 3x²

f'(x) = 3 + 3x²

15 = 3 + 3x²

switch sides

3 + 3x² = 15

3x² = 15-3

3x² = 12

Divide both sides by 3

x² = 4

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$x=\sqrt{4},\:x=-\sqrt{4}$

$x=2,\:x=-2$

Thus, the value of x will be:

$x=2,\:x=-2$

5 0

3 years ago

15. Aunt Bev baked 94 cookies to make goody

ICE Princess25 [194]

It depends on how many bags she has! Then subtract that

3 0

3 years ago

Read 2 more answers

I need help how to do this. Please help

earnstyle [38]

The best method would be to cross-multiply. Multiply the figure on the top left with the bottom right. Then set it equal to the multiplication of the bottom left with the top right.
This would turn into:
-1(x-1)=2(x+3) Then distribute the multiplication through the parentheses.
-x+1=2x+6 Next, get all the variables on one side, and the integers on another.
2x+x=1-6
3x= -5
x= -5/3

8 0

3 years ago

What are the extremes of the following proportion? 3⁄15 = 12⁄60

pashok25 [27]

<u>Answer:</u>

3 and 60

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

For the given proportions, $\frac { 3 } { 15 } = \frac { 12 } { 60 }$ , 3 and 60 are the extremes while 12 and 15 are the means.

To understand this, we can take a look at an example.

Suppose two ratios a:b and c:d are in proportion.Then it can be expressed as :

$ab=cd$

Here, a and d are the extreme ends and b and c are the means.

6 0

3 years ago

Parallelogram Q T S R is shown. Sides Q T and R S are parallel, and sides Q R and T S are parallel. Angle Q is (9 x minus 6) deg

jenyasd209 [6]

Answer:

m<Q = 93 degrees

m<R = 87 degrees

Step-by-step explanation:

Given the following angles;

m<Q = 9x-6

m<R = 8x-1

Looking at Devin's work, we will see that he the sum of both angles is 180 degrees

Hence m<Q + m<R = 180

9x - 6 + 8x - 1 = 180

9x+8x-6-1 = 180

17x - 7 = 180

17x = 180 + 7

17x = 187

x = 187/17

x = 11

Get m<Q

m<Q = 9x - 6

m<Q = 9(11) - 6

m<Q = 99 - 6

m<Q = 93 degrees

Get m<R

m<R = 180 - m<Q

m<R = 180 - 93

m<R = 87degrees

8 0

3 years ago

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