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]
3 years ago
13

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

Mathematics
1 answer:
Verdich [7]3 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
Of the cakes at Naomi's Bakery, 1/6 have chocolate frosting. Of the cakes with chocolate frosting, 1/5 have raspberry filling. W
Sever21 [200]

Answer:

\frac{1}{6}  \times  \frac{1}{5 }  \\  \frac{1}{30}

5 0
3 years ago
Find the measure of the hands of a clock at 12:38
Vinvika [58]
I would say 12 hours and 38 min
8 0
3 years ago
Order of operations what should be done first to evaluate 6+ (-5-7) ÷ 2 -8(3)
Maru [420]

Answer:-24

Step-by-step explanation:

6+(-5-7) ➗ 2-8(3)

6-12 ➗ 2-24

6-6-24

0-24=-24

3 0
3 years ago
I need x+y=5 and y=2x-4solved algebraically
schepotkina [342]

Answer:

x = 3; y = 2

Step-by-step explanation:

x + y = 5

y = 2x - 4

<em>Isolate the y in the first equation</em>

y = 5 - x

y = 2x - 4

<em>Substitute the values</em>

5 - x = 2x - 4

<em>Isolate the Variable</em>

9 = 3x

<em>Simplify</em>

3 = x

<em>Plug that into the first equation</em>

3 + y = 5

<em>Subtract 3 from both sides</em>

y = 2

4 0
3 years ago
Read 2 more answers
Find the measure of the missing angles in the kite​
ser-zykov [4K]

Answer:

x = y = 104°

Step-by-step explanation:

The sum of the interior angles = 360°

The opposite angles x and y are congruent , that is y = x , then

92 + 60 + x + x = 360

152 + 2x = 360 ( subtract 152 from both sides )

2x = 208 ( divide both sides by 2 )

x = 104

Then

x = y = 104°

7 0
2 years ago
Other questions:
  • Which choices are correctly written in a scientific notation ? select the four correct answers
    5·1 answer
  • NEED HELP ASAP!!!
    8·1 answer
  • The age of a dog (x) can be compared to the age of a human being (y) by the equation 7y = x. Some dogs have reportedly lived for
    10·2 answers
  • Solve the following equation<br> 1/3 a = -5
    5·1 answer
  • Please someone help me! I know that the answer is close to 17, so if u know the answer please show me how to do it!
    10·1 answer
  • Find the value of x and y
    15·1 answer
  • Select the correct answer. Function f is an exponential function that has an initial value of 64 and decreases by 50% as x incre
    5·2 answers
  • can anyone help solve this with a detailed explanation so my older sister can find out how to do it ​
    5·1 answer
  • Can someone help me!!
    12·1 answer
  • Find the intercepts and graph the equation. 7x +5y=12
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!