1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nana76 [90]
3 years ago
13

Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x3 − 27x + 3 (a) Find the interval of increase. (E

nter your answer using interval notation.)

Mathematics
1 answer:
xxTIMURxx [149]3 years ago
6 0

Answer:

(-∞,-3) and (3,∞)  

Step-by-step explanation:

f(x) = x³ − 27x + 3

1. Find the critical points

(a) Calculate the first derivative of the function.

f'(x) = 3x² -27  

(b) Factor the first derivative

f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)

(c) Find the zeros

3(x + 3) (x - 3) = 0

x + 3 = 0      x - 3 = 0

     x = -3          x = 3

The critical points are at <em>x = -3</em> and x = 3.

2. Find the local extrema

(a) x = -3

f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57

(b) x = 3

f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51

The local extrema are at (-3,57) and (3,-51).

3, Identify the local extrema as maxima or minima

Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)

f'(-4) = 3x² -27 = 3(4)² - 27  = 21

f'(0) = 3(0)² -27 = -27

f'(4) = 3(4)² - 27 = 51

The function is increasing on the intervals (-∞,-3) and (3,∞).

The graph below shows the critical points of your function.

You might be interested in
Talia used 1/3 of a piece of wood for the base of her project 1/4 of the piece of wood for the vertical support and the rest for
Veseljchak [2.6K]

Answer:

The fraction of wood used for horizontal support is \frac{5}{12}.

Step-by-step explanation:

Assume that the total piece of wood is of length 1.

It is provided that Talia used \frac{1}{3} of the piece of wood for the base of he project.

She use \frac{1}{4} of the piece of wood for the for the vertical support.

The remaining wood she used for horizontal support.

The amount of wood used for horizontal support can be computed by the subtracting the amount of wood used for base of the project and vertical support form 1.

Compute the amount of wood used for horizontal support as follows:

Horizontal\ support=1-Base\ of\ project-Vertical\ support\\= 1 - \frac{1}{3}-\frac{1}{4}\\  =\frac{12-4-3}{12} \\=\frac{5}{12}

Thus, the fraction of wood used for horizontal support is \frac{5}{12}.

3 0
2 years ago
If you get this, you are a critical thinker. I enter the garden. There are 34 people. You kill 30. How many people are in the ga
Elena L [17]

Answer:

Step-by-step explanation:

is it 34 because you haven't moved the bodies. however including you there's 35???

3 0
3 years ago
Read 2 more answers
3. Your friend shows you a scale drawing of her apart-
andrey2020 [161]

Answer:

The answer is 20 feet

Step-by-step explanation:

We know that her apartment sketch is 6 by 4 inches.

If the 6 inch side is actually 30 feet and 6 goes into 30 5 times, we should multiply 4 by 5 to get proportionate answers.

Therefore her apartment is 20*30 feet

Hope this helps

8 0
2 years ago
What is the solution set of x2 + 5x - 5 = 0?
Llana [10]

If you're completing the square the answer is in the image.

expression

x^2 + 5x - 5=ax^2+bx+c

a=1, b=5, c=-5, and you can solve it that way.

4 0
3 years ago
What is the solution set of (x - 2)(x - 3) = 2?
Deffense [45]

Answer:

X = 4, 1

Step-by-step explanation:

Multiplying out

X^2 - 2x - 3x +6 = 2

X^2 - 5x +4 = 0

Factoring:

X^2 - 4x - X +4

X(x-4) - 1(x-4)

(x-1)(x-4)=0

X= 1, 4

8 0
2 years ago
Other questions:
  • What is the value of y when x = 6? -3x + 9y = 18
    5·2 answers
  • How much is 2.billion in fraction form
    10·2 answers
  • The best description of the AA Rule is:
    15·1 answer
  • 4.<br> What is the domain of the graph shown below?
    15·2 answers
  • Jeremy mowed several lawns to earn money. After he paid $17 for gas, he had $75 leftover. How much did he earn?
    8·1 answer
  • What is the volume of a sphere with a diameter of 6.3 rounded to the nearest tenth
    9·2 answers
  • WILL GIVE BRAINLIEST!!!!! 100 POINTS
    10·2 answers
  • Us the expression (8x + 2) + (- 9x + 7)
    11·1 answer
  • How are percents greater than 100% used in real world contexts
    11·1 answer
  • Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic tit
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!