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
Radda [10]
2 years ago
13

On what interval is the functioning decreasing m(x)=4x^3-5x^2-7x?

Mathematics
1 answer:
Verdich [7]2 years ago
4 0
M(x) = 4x^3 - 5x^2 - 7x
Let us first find the zeros of the function.
That is when it is equal to zero.

m(x) = 4x^3 - 5x^2 - 7x  = 0
x(4x^2 - 5x - 7) = 0.  Therefore x = 0 or 4x^2 - 5x - 7 = 0.
Using a quadratic function calculator to solve 4x^2 - 5x - 7
x = 2.09, -0.84
Therefore the zeros are x =-0.84, 0, 2.09 for the function m(x).

The intervals observed are imagining  that the zeros are on the number line:
x<-0.84,    -0.84<x<0,  0<x<2.09,  x>2.09.

For each of this range we would test the function with a number that falls in the range.

The function is decreasing in the interval where it is less than 0.
For x<-0.84, let us test x = -1, m(x) = 4x^3 - 5x^2 - 7x = 4(-1)^3 - 5(-1)^2 - 7(-1) = -4 -5 +7 = -2,    -2 < 0, so it is decreasing here.

For  -0.84<x<0, let us test x = -0.5, m(x) = 4x^3 - 5x^2 - 7x = 4(-0.5)^3 - 5(-0.5)^2 - 7(-0.5) = -0.5 -1.25 +3.5 = 1.75,  1.75 >0. It is not decreasing.


For  0<x<2.09, let us test x = 1, m(x) = 4x^3 - 5x^2 - 7x = 4(1)^3 - 5(1)^2 - 7(1) = 4 -5 -7 = -8,  -8 <0. It is decreasing.

For  x>2.09, let us test x = 3, m(x) = 4x^3 - 5x^2 - 7x = 4(3)^3 - 5(3)^2 - 7(3) = 108 -45 -21 = 42,  42 >0. It is not decreasing.

So the function is decreasing in the intervals:

x < -0.84,  & 0<x<2.09.

You might be interested in
Three moons are in the same circular orbit around a planet. The moons are each 115,000 kilometers from the surface of the planet
marshall27 [118]
275,000 km
The moons A, B, C form a right triangle with AC forming a hypotenuse with the diameter of the planet and the distance of both moons from the surface. So add A to the surface, plus the diameter of the planet, plus surface to c.
115000+45000+115000 = 275000
7 0
2 years ago
Read 2 more answers
Is x = 3 a solution to the equation x + 7 = 11?
olya-2409 [2.1K]

Answer:

A

Step-by-step explanation:

3+7 is 10, not 11. Therefore, x cannot be 3.

3 0
2 years ago
Read 2 more answers
What number set does -3.8 belong in
Lerok [7]

Answer:

real number and rational number

Step-by-step explanation:

I infer that by number set you mean what kind of number it is. It is real because it is -3.8 and rational because it is terminating. It is not a integer, whole number, or natural number because -3.8 is a decimal

8 0
3 years ago
The total cost in dollars to buy calculator sets for the students in Mr. Engle’s math class can be found using the function C =
DedPeter [7]

Answer:

A

Step-by-step explanation:

75.95*27+12.25= 2062.9

2062.9 is the minimum

7 0
2 years ago
Read 2 more answers
R = 2m<br> 3 m<br> es<br> What is the surface area of this cylinder? (rounded to nearest tenth)
marysya [2.9K]

Answer:

We can conclude that the surface area of the prism is 71 square meters.

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • A cylindrical oil from has a diameter of 2ft and a height of 3 feet. What is the volume of the oil drum?
    8·1 answer
  • Need help asap please! If f(x)=7x and g(x)=3x+1 find (f o g)(x) A.10x+1 B.21x+1 C.21x^2+7x D.21x+7
    12·2 answers
  • HELP ASSAP WITH THIS QUESTION!!!!!!
    14·2 answers
  • Mario spent $23.85 at the bookstore on one book and some magizines. The book cost $12.60 and the magizines cost $2.25 each. How
    8·1 answer
  • The O'Niell family decided to book a hotel for a trip to Orlando, FL from Saturday 6/3 through Friday 6/9. They decide to stay a
    5·1 answer
  • Can someone please help me ASAP
    11·1 answer
  • Find f(100) and show how to solve
    7·1 answer
  • Jason has 2 pizzas that he cuts into fourths how many 1/4-size pizzas does he have
    10·1 answer
  • If Luis can type 168 words in 4 minutes, what is his speed per minute?
    15·2 answers
  • Please help me with this
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!