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
Anettt [7]
3 years ago
11

Dealing with concave upward and downward. also intervals increasing and decreasing. How do work these problems out.

Mathematics
1 answer:
asambeis [7]3 years ago
7 0

Answer:

increasing from (-∞, -3)∪(3, ∞)

decreasing from (-3, 3)

concave up from (0, ∞)

concave down from (-∞, 0)

Step-by-step explanation:

The derivative gives you the slope of the function, so to find where the graph is increasing, find the derivative of f(x).

  • A positive derivative, f'(x)>0, means it's increasing,
  • A zero derivative, f'(x)=0, means the slope is flat.
  • A negative derivative, f'(x)<0, means it's decreasing

So solve for when the derivative is 0 and plug in random number into x and see if it's positive or not.

I had x=-3 and x=3 for f'(x)=0. So i plug a number below x=-3

I chose x=-∞ and got f'(-∞)=(-∞)²-27 = ∞ which is a positive number, so the slope is increase when x<3.

Then I chose a number between x=3 and x=3.

I chose x=0 and got f'(0)=(0)²-27 =-27 which is a negative number, so the slope is decreasing when -3<x<3.

Then I chose a number greater than x=3.

I chose x=∞ and got f'(∞)=(∞)²-27 = ∞ which is a positive number, so the slope is increase when x>3.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To find if it concave up or down, find the second derivative. The solving process is the same as described in the previous paragraphs.

  • If the second derivative is positive, f''(x)>0, it concave up
  • If the second derivative is zero, f''(x)=0, it doesn't concave at all
  • If the second derivative is negative, f''(x)<0, it concave down

You might be interested in
What is the value of 2(x+y)² when X=3 and Y=4 ?
otez555 [7]

Answer:

98

Step-by-step explanation:

Step 1: Define

2(x + y)²

x = 3

y = 4

Step 2: Substitute and Evaluate

2(3 + 4)²

2(7)²

2(49)

98

3 0
3 years ago
Read 2 more answers
No-Freeze antifreeze mixture contains 30% alcohol. How much alcohol is there in 15 quarts of No-Freeze
Vikki [24]

Not clear.

Step-by-step explanation:

How much does the original mixture produce? is the original 1 quart? 1 gallon? 1 cup?

5 0
2 years ago
What is the total number of the side on 8 triangle
Lelu [443]
Total number of triangle is 632
With 3 diagonal endpoints are 56
5 0
3 years ago
Read 2 more answers
may somone give me the answers with question 3 4 and 5. one BRAINLIEST IF SOMONE CAN ANSWER AND FIVE STAR​
Gnoma [55]

Answer:

Well, we need a definition or length/width of the figure of it first, let me see what I can find, I'll leave it in my replies.

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
A=1/2h(B+b); A=15, B=4,b=1
suter [353]

step by step

A=1/2h(B+b)

15=1/2h(4+1)

15/(4+1)=1/2h

15/5=1/2h

3=1/2h

h=2*3

h=6

4 0
2 years ago
Other questions:
  • Janine can use up to 150 one-inch blocks to build a solid, cube-shaped model. What are the dimensions of the possible models tha
    13·2 answers
  • Which equation represents a line which is perpendicular to the line y=-3/7x+4
    15·1 answer
  • How do you solve 3x+1 = 15 for x using the change of base formula log base b of y equals log y over log b?
    13·2 answers
  • What are the next two terms after 12, 0.5, 6, 3, 18, ....?
    15·2 answers
  • Translate the following statement into a mathematical equation: The product of four and a number, plus six, is eighteen.
    11·2 answers
  • How many solutions does this system of equations have?
    13·2 answers
  • Бу^5 + 4 y^4 - 3у^3-1 by (3 y^2 - y+1​
    9·1 answer
  • Is it ok if you help me solve this?
    13·2 answers
  • What is value of x?<br> Enter your answer in the box.<br> x =
    7·2 answers
  • 5. Graph the hyperbola ya<br> 16<br> What are the equations of the asymptotes?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!