If ƒ (x ) = 3x2 - x, find ƒ (-2).

Answer:

x=1=2y

Step-by-step explanation:

Answer:

We have the function:

f(x) = 3*x^5 - 4*x^3 - 3*x

To find the maximum/minimums, we first need to look at the roots of the first derivative of f(x), this is:

f´(x) = 5*3*x^4 - 3*4*x^2 - 3

f´(x) = 15*x^4 - 12*x^2 - 3

We can do the change of variable:

u = x^2

Then we can rewrite:

f'(u) = 15*u^2 - 12*u - 3

This is a quadratic equation, the solutions will be obtained by the Bhaskara´s equation:

So the solutions are:

[tex]u = \frac{+12 +- \sqrt{(-12)^2 - 4*(-3)*15} }{2*15} = \frac{12 +- 18}{30}[/tex]

Then the two solutions are:

u = (12 + 18)/30 = 1

this leads to:

x^2 = 1, then we can have x = ± 1

the other solution is:

u = (12 - 18)/30 = -6/30 = -(1/5)

and x^2 = -(1/5), then:

x = ±√(1/5)*i

So those are the possible values for the minimum/maximums.

Now to see it, we need to look at the second derivative ad see iff:

f´´(x) > 0 then x is a minimum

f''(x) < 0, then x is a maximum.

We have that:

f´´(x) = 4*15*x^3 - 2*12*x

f´´(x) = 60*x^3 - 24*x

Notice that the two complex roots will lead to complex values of f(x), so these can be ignored here, then we have to try only with x = ± 1.

f´´(1) = 60*1^3 - 24*1 = 36

then x = 1 is a minimum.

f´´(-1) = 60*(-1)^3 -24*-1 = -36

then x = -1 is a maximum.

Then we can conclude that the relative maximum is at x = -1

The function f given by [tex]f(x) = 3x^5-4x^3-3x[/tex] has a relative maximum at

x = -1

The given function is:

[tex]f(x) = 3x^5-4x^3-3x[/tex]

Find the derivative of the function:

[tex]f'(x)=15x^4-12x^2-3[/tex]

Find the critical points by equation f'(x) to zero

[tex]15x^4-12x^2-3=0\\\\5x^4-4x^2-1=0[/tex]

By solving the equation above, the critical points are:

x = -1,  x =  1

Find the second derivative of f(x)

[tex]f''(x)=60x^3-24x[/tex]

[tex]f''(-1)=60(-1)^3-24(-1)\\\\f''(-1)=-36[/tex]

Since f''(-1) < 0, x = -1 is a maximum point

[tex]f''(1)=60(1)^3-24(1)\\\\f''(1)=36[/tex]

Since f''(1) > 0, x = 1 is a minimum point

Therefore, the function [tex]f(x) = 3x^5-4x^3-3x[/tex] has a relative maximum at x = -1

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Answer:

Small: 7

Large:13

Step-by-step explanation:

I worked it out, hope this helps

Answer:

Answer:

Small: 7

Large:13

Step-by-step explanation:

I worked it out, hope this helps

Answer:

You have 3 eggs.

Step-by-step explanation:

You "had" 4 eggs, those  do not count.  A thief then gave you 3 eggs. And lastly, a rooster does not lay eggs. In conclusion, you have 3 eggs.

The total number of eggs he finally has as inferred from the riddle is 3 eggs.

Evaluating each sentence :

If I had 4 eggs ; This is an imagination, hence, the speaker was only imagining if he had. Hence, total here is 0

A thief gave out 3 eggs ; Hence, the total number of eggs = (0 + 3) = 3 eggs

Farm Rooster laying 5 eggs is impossible S Farm roosters do not lay eggs. Number of eggs here is 0.

Hence, the total number of eggs = (0 + 3 + 0) = 3 eggs.

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Answer:

-25, or a

Step-by-step explanation:

Answer:

slope-intercept form is y=mx+b so

y=0x+5

or

y=5

Answer:

4n - 3

Step-by-step explanation:

N + 3 (n - 1)

N + 3n - 3

4n - 3 is the final answer  

hope that helps :))

Answer:

y= -5x-3

Step-by-step explanation: Hope this helped!!!

btw can i have brainliest?

Answer:

30

Step-by-step explanation:

Well round 902 down to 900, then round down 31 to 30.

Therefore 900 divided by 30 is 30.

So an estrimate answer to 902 divided by 31 is 30.

Answer: +15

Step-by-step explanation: A deposit of $15 is an increase,

which means that it's positive.

So it can be written as +15.

Answer: 82

Step-by-step explanation:

Answer:

0.2611

Step-by-step explanation:

We have x to be binomially distributed random variable which denotes the items number that are defective

We have been given n = 59 as our sample size

Probability of 5% = probability of success

1-5% = 0.95

We solve using this formula

nCxP^xq^n-x

= 50C2(0.05)²(0.95)^50-2

= 0.2611

This is the probability that exactly 2 would be defective

Answer: 1/4 or 0.25.

Step-by-step explanation: 2/4 x 4/8 = 8/32 = 1/4 = 0.25.

Answer:

1/4 or 0.25

Step-by-step explanation:

2/4 * 4/8 =

2*4=8 and 4*8=32

so 2/4 * 4/8 = 8/32

8/32 = 1/4 = 0.25

So the answer is:

1/4 or 0.25

Answer:

y = 23.14 ft

x = 15.56 ft

so the dimensions of the building will be = 15.56 ft x 15.56 ft x 23.14 ft

Step-by-step explanation:

the area of the roof = xy

cost of the roof = 11xy

the area of the sides and back = 2xy + x²

cost of the sides and back = 14(2xy + x²) = 28xy + 14x²

area of the glass front = x²

cost of the glass front = 15x²

minimize:

total cost = 11xy + 28xy + 14x² + 15x² = 39xy + 29x²

total volume = x²y = 5600 ⇒ constraint

39y + 58x = 2λxy

39x = λx2

x²y = 5600

λx = 39 which we replace into the first equation

39y + 58x = 78y

58x = 39y

(58x)²y = 58² · 5600

now we replace 58x by 39y

(39y)²y = 58² · 5600

39² · y³ = 58² · 5600

y³ = (58² · 5600) / 39² = 12,385.53583

y = ∛12,385.53583  = 23.14 ft

x² = 5600/ 23.14 = 242.04

x = 15.56 ft

Answer:

The option that are correct is  option a and  option c

Step-by-step explanation:

From the question we are told that

   The sample space is  n =  6 (i.e six sides)  

     The number of even numbers in the sample space is  k  = 3 (i.e  2,4, 6)

Generally the probability of rolling an even number with a six-sided, equally weighted die is mathematically represented as

       [tex]P(E) = \frac{3}{6}[/tex]

=>     [tex]P(E) = \frac{1}{2}[/tex]

Answer:

4,19,79,320,1284

Step-by-step explanation:

Answer:

6u²−3uv²−4u⁴+5uv

Step-by-step explanation:

i had a test with this and got it right

Answer:

The fewest amount of boxes would be 10

Step-by-step explanation:

I added the 25 red flowers to the 13 flowers and got 38. I then divided 38 by 4 getting 9.5. 9.5 isn't a full box so I rounded to the decimal and got 10.

I hope this what you were looking for.

Using a arithmetic operations , the fewest number of boxes Ethan will need to plant all the flowers ls 10

Creating a

Total number of flowers to be planted :

Total number of flowers = 25 + 13 = 38 flowers

Number of flower boxes = (total number of Flowers ÷ number of flowers per box)

Number of flower boxes = (38 ÷ 4) = 9.5 flower boxes

Therefore, the fewest number of boxes that will be needed is 10.

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Answer:

Third side is 15cm. Perimeter is 37cm.

Step-by-step explanation:

In a triangle sum of two sides is always greater than third side. Two sides of a isosceles triangle are equal.

So if the third side is 7cm

7+7=14cm which is less than 15 cm.

hence third side is 15 cm as

15+15=30cm which is greater than 7cm

15+7=22cm which is greater than 12cm

then

perimeter=15+7+15=37cm

Answer:

5

Step-by-step explanation:

just look at the graph

Answer: 1/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

3y > 2x + 12

[tex]y>\frac{2}{3}x+4[/tex]

This inequality will be represented by the a dotted line and solution area for the inequality will be shaded area (In red) above the dotted line.

2x + y ≤ -5

y ≤ -2x - 5

This inequality will be represented by a solid line and solution area will be the shaded area (in blue) below the solid line.

Therefore, common area of both will be the solution area for the system of inequalities.

Plotting the inequalities using geogebra online graphing calculator. The graph is attached

Inequalities is an expression used to show the non equal comparison of numbers and variables.

Given the system of inequalities:

3y > 2x + 12

3y - 2x > 12   (1)

2x + y < -5    (2)

Plotting the inequalities using geogebra online graphing calculator. The graph is attached

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Answer: 0 and 4

Step-by-step explanation:

First blank zero, second blank 4

Answer:

If you have to do the sliders problem the answeres in order are, set a to -3, set b to 2 and keep c at 0.

Step-by-step explanation:

the correct answer is y=-3 sin(2x) and the equation from the sliders should match the answer.

y=-3 sin(2x) is the equation has a maximum at (0, –1) and a minimum at ( pi Over 3, negative 5)

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

We need to use the sliders to change the values of a, b, c, and d in the cosine function.

We need to find the equation which has maximum at (0, –1) and a minimum at (pi Over 3, negative 5)).

While doing slider problems we have to set the values as set a to -3, set b to 2 and keep c at 0.

y=-3 sin(2x) is the answer and the equation from the sliders should match the answer.

Hence y=-3 sin(2x) is the equation has a maximum at (0, –1) and a minimum at ( pi Over 3, negative 5)

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