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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.

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Answer:

$11,714

Step-by-step explanation:

C(x) = 0.7x² - 462x + 87,944

this is a quadratic equation that opens up

the vertex will be the minimum

From the quadratic formula the x coordinate of the vertex is

x = -b/2a

x = 462/(2 * 0.7)

x = 330

Plug in

c(330) = 0.7(330²) - 462(330) + 87,944

c(330) = 11,714

$11,714

5 0
3 years ago
hank has a triangular rug in his bedroom. the perimeter of the rug is 14 feet . two of the side lengths are 6 feet . what is the
Mariana [72]

Answer:

The 3rd side of the rug is 2 ft long

Step-by-step explanation:

6+6=12

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3 years ago
The sum of two consecutive even integers is at most seven more than half the sum of the next two consecutive even integers
Pavel [41]

The sum of two consecutive even integers is at most seven more than half the sum of the next two consecutive even integers

two consecutive even integers: n, n+2

next two consecutive even integers n+4, n+6

n+(n+2) >= 7+1/2(n+4 +n+6)

combine like terms

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3 years ago
What is true about the completely simplified sum of the polynomials 3x2y2 − 2xy5 and −3x2y2 + 3x4y?
Assoli18 [71]

Answer:

The sum is a binomial with a degree of 6

Step-by-step explanation:

we have

(3x^{2}y^{2}-2xy^{5})+(-3x^{2}y^{2}+3x^{4}y)

Group terms that contain the same variable

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0-2xy^{5}+3x^{4}y

-2xy^{5}+3x^{4}y

The sum is a binomial ( two terms) with a degree of 6  

-2xy^{5} has a degree of 6 (x has an exponent of 1, y has 5, and 1+5=6)

6 0
3 years ago
Read 2 more answers
Please help with all, I’ll mark brainliest as long as you tell me how you got that answer.
Mumz [18]

Answer:

function= 2nd,6th

not a function=1st,3rd,4th,5th

Step-by-step explanation:

because in graphing a function, there should only be one y for the x. 2 or more y's in one x is considered as not a function

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