A cake shop offers circular cakes with diameters of 8 in., 12 in., and 15 in. Identify the area of each cake

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

2 years ago

What's your real rate of return if your savings account pays 2.5% interest and inflation is at 1%?

kolbaska11 [484]

Answer:

Real rate of return = 1.5%

Step-by-step explanation:

Given:

Savings account return = 2.5%

Inflation rate = 1%

Find:

Real rate of return = ?

Computation:

⇒ Nominal rate of return = Real rate of return + Inflation rate

⇒ Real rate of return = Savings account return - Inflation rate

⇒ Real rate of return = 2.5% - 1%

⇒ Real rate of return = 1.5%

6 0

3 years ago

A mathematical formula designed to predict population fluctuations in a community could be called a(an)

kvasek [131]

It would be called an ecological model.

5 0

3 years ago

Jasmine recorded the number of minutes she spent doing homework each day during the months of March and April.

larisa [96]

Answer:

5647

Step-by-step explanation:

You go to the store and get some chips to kill your dad

6 0

2 years ago

In the diagram shown of circle A, tangent MB is drawn along with chords BAC and BF . Secant MFE intersects BAC at G. It is known

mote1985 [20]

Answer:

arc BF = 76°
∠M = 31°
∠BGE = 121°
∠MFB = 111°

Step-by-step explanation:

(a) ∠FBM is the complement of ∠FBC, so is ...

∠FBM = 90° -52° = 38°

The measure of arc BF is twice this angle, so is ...

arc BF = 2∠FBM = 2(38°)

arc BF = 76°

__

(b) ∠M is half the difference between the measures of arcs BE and BF, so is ...

∠M = (1/2)(138° -76°) = 62°/2

∠M = 31°

__

(c) arc FC is the supplement to arc BF, so has measure ...

arc FC = 180° -arc BF = 180° -76° = 104°

∠BGE is half the sum of arcs BE and FC, so is ...

∠BGE = (1/2)(arc BE +arc FC) = (138° +104°)/2

∠BGE = 121°

__

(d) ∠MFB is the remaining angle in ∆MFB, so has measure ...

∠MFB = 180° -∠M -∠FBM = 180° -31° -38°

∠MFB = 111°

3 0

3 years ago