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
pishuonlain [190]
2 years ago
12

PLEASE HELP?

Mathematics
1 answer:
const2013 [10]2 years ago
6 0

Answer:

When we have a function g(x)

We will have a maximum at x when:

g'(x) = 0

g''(x) < 0.

Now we start with:

g(x) = 3*x^4 - 8*x^3

The first derivation is:

g'(x) = 4*3*x^3 - 3*8*x^2

g'(x) = 12*x^3 - 24*x^2

We can rewrite this as:

g'(x) = x^2*(12*x - 24)

Now we want to solve:

g'(x) = 0 =  x^2*(12*x - 24)

We have one trivial solution, that is when x = 0.

The other solution will be when the term inside of the parentheses is equal to zero.

Then we need to solve:

12*x - 24 = 0

12*x = 24

x = 24/12 = 2

Then g'(x) is equal to zero for x = 0, and x = 2.

Notice that both of these points are included in the interval [ -2,2 ]

Now we need to look at the second derivative of g(x):

g''(x) = 3*12*x^2 - 2*24*x

g''(x) = 36*x^2 - 48*x

Ok, now we need to evaluate this in the two roots we found before:

if x = 0:

g''(0) = 36*0^2 - 48*0 = 0

g''(0) = 0

Then we do not have a maximum at x = 0, this is a point of inflection.

if x = 2:

g''(2) = 36*(2^2) - 48*2 = 48

then:

g''(2) > 0

This is an absolute minimum.

Now let's look only at the interval [ -2,2 ]

We know that:

g''(0) =  0

g''(2) > 0

Then at some point, we should have g''(x) < 0 in our interval.

We need to find the first point such that happens, so let's try with the lower limit of the interval but with the first derivation, if g'(x) < 0, this means that the function is decreasing from that point on, then that point will be a maximum in our interval.

x = -2

g'(-2) = (-2)^2*(12*-2 - 24) = -192

And if we look at the function:

g'(x) = x^2*(12*x - 24)

We can easily see that it is negative unitl x = 0, and then it keeps being negative until x = 2.

So in the interval  [ -2,2 ], the function g'(x) is always negative or zero, this means that in the interval  [ -2,2 ], the function g(x) is always decreasing or constant.

Then the absolute maximum of g(x) in the interval  [ -2,2 ]  will be  x = -2

this means that:

g(-2) ≥ g(x) for all x ∈  [ -2,2 ]

You might be interested in
180000000 plus 137473735858686858686 plus 17647657
ICE Princess25 [194]

Answer:

137473735858884506343

Step-by-step explanation:


3 0
3 years ago
Read 2 more answers
Please help anybody due in LESS THAN 1 MIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
maxonik [38]

Answer:

distance was 35 units and the average speed was 5 units per minute

Step-by-step explanation:

-47--12=-35

the absolute value of -35 is 35

35 units took 7 minutes

so 1 unit takes 35/7 minutes= 5 minutes

8 0
3 years ago
<img src="https://tex.z-dn.net/?f=p%5E%7B3%7D%20at%20%5C%5C%5C%5C%20p%20%3D%202" id="TexFormula1" title="p^{3} at \\\\ p = 2" al
WITCHER [35]
<h3>Answer:  8</h3>

Reason:

Replace p with 2 and evaluate.

p^3 = 2^3 = 2*2*2 = 8

Think of a cube that is 2 units along each side. It's volume is 2*2*2 = 8 cubic units. Repeated multiplication can be shortened to using exponents.

Another example: 7^4 = 7*7*7*7

6 0
1 year ago
Sharon and Jacob started at the same place. Jacob walked 3 m north and then 4 m west. Sharon walked 5 m south and 12 m east. How
Ilya [14]

Consider the coordinate plane:

1. The origin is the point where Sharon and Jacob started - (0,0).

2. North - positive y-direction, south - negetive y-direction.

3. East - positive x-direction, west - negative x-direction.

Then,

  • if Jacob walked 3 m north and then 4 m west, the point where he is now has coordinates (-4,3);
  • if Sharon walked 5 m south and 12 m east, the point where she is now has coordinates (12,-5).

The distance between two points with coordinates (x_1,y_1) and (x_2,y_2) can be calculated using formula

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.

Therefore, the distance between  Jacob and Sharon is

D=\sqrt{(12-(-4))^2+(-5-3)^2}=\sqrt{16^2+8^2}=\sqrt{256+64}=\sqrt{320}=8\sqrt{5}\approx 11.18\ m.

7 0
3 years ago
Which expression has the same value as 12 − 6 ÷ 3
Juli2301 [7.4K]
Answer is a.
Due to BIDMAS/BODMAS
anything that is first, in this case division, goes into brackets.
6 divided by 3 would go into brackets making you solve that first then u would subtract your answer by 12 making your answer 4

Answer is a.

a.
5 0
2 years ago
Read 2 more answers
Other questions:
  • carl needs to take 2 pairs of jeans and 4 shirts for every 4 days he spends at church. He spends 14 days.
    12·1 answer
  • Help me on these and please explain ASAP
    15·1 answer
  • 2.<br> Solve for y.<br> y/8 = 8
    15·1 answer
  • Which equation represents a line that passes through (4.) and has a slope of
    15·1 answer
  • Find the height of a door on a scale drawing if the door is 2 meters tall and the scale is 1 centimeter = 4 meters. Round to the
    15·1 answer
  • A 168-inch board is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
    14·1 answer
  • There are 15 boys and 12 girls in Rosemary’s class. One of the students is selected at random to be the class monitor. What is t
    8·1 answer
  • What is the value of x for the parallelogram shown?<br> A. 30<br> B. 75<br> C. 60<br> D. 15
    6·1 answer
  • Pick number 1-10 if you get it right ill pay 50 dollas
    6·1 answer
  • Please can someone help with this
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!