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
weqwewe [10]
3 years ago
9

State the restrictions on the range for y=x^4+8x^3+k

Mathematics
1 answer:
sveticcg [70]3 years ago
3 0
Answer: The range is y \ge k-432

The way to get this answer isn't completely obvious. What I did first was graph the function using GeoGebra allowing k to be a parameter. With k as a sliding parameter, the graph was able to be slid up and down the screen. The basic shape of the curve is a distorted W shape. The lowest point being the local minimum. Which is where the lower endpoint of the range would be.

Using the derivative, we can get
y = x^4 + 8x^3 + k
dy/dx = 4x^3 + 24x^2
set dy/dx equal to zero and solve for x
dy/dx = 0
4x^3 + 24x^2 = 0
4x^2(x + 6) = 0
4x^2 = 0 or x+6 = 0
x = 0 or x = -6

It turns out that x = 0 is a saddle point so we can ignore this value. Only x = -6 is where the local min is at. Plug this back into the original function

y = x^4+8x^3+k
y = (-6)^4+8(-6)^3+k
y = -432+k
y = k - 432

So when the input is x = -6, the output is k - 432 for some value k
In other words, the smallest y can get is k - 432. Otherwise it will be larger than this value

So that's why the range is y \ge k - 432

Note: if this calculus approach doesn't make much sense, then you can try various k values and use a calculator to find the lowest point. Making a table of k values with the corresponding lowest point would hopefully point you in the right direction. 
You might be interested in
A flower vase bought for Rs. 72 and sold for Rs. 63. Find the loss percent.​
nasty-shy [4]

Answer:

12.5% is loss....

hope it helps.

3 0
3 years ago
Read 2 more answers
The market bought grapes for $0.87 a pound and sold them for $1.15 a pound. What is the percent of increase rounded to the neare
KatRina [158]
43.7% 
<span>
Difference = 115 - 87 = $0.38
Use 87 as the base because that's the price to start
38/87 = 0.43678</span>
5 0
3 years ago
I'm not quite sure how to get the area of this parallelogram. ​
DENIUS [597]

Answer:A=224

Step-by-step explanation:

A=bh

A=Area B=Base H=Height

A=16*14

7 0
3 years ago
Yolanda opened a retirement account earning 5.5% interest per year, compounded monthly. She deposited $100 each month. Assume th
Naya [18.7K]

The balance in dollars and cents in Yolanda's account at the end of 4 years is $5,355.29

What is the future value of an ordinary?

An ordinary annuity is the one where the monthly deposit occurs at the end of each month rather than at the beginning of the months such its future value based on 5.5% annual interest rate can be determined thus:

FV=PMT*(1+r)^N-1/r

FV=balance in dollars and cents in Yolanda's account at the end of 4 years=unknown

PMT=monthly deposit=$100

r=monthly interest rate=5.5%/12=0.00458333333333333

N=number of monthly deposits in 4 years=4*12=48

FV=$100*(1+0.00458333333333333)^48-1/0.00458333333333333

FV=$5,355.29

Find out more about future value on:brainly.com/question/20187354

#SPJ1

Missing question:

What was the balance in dollars and cents in Yolanda's account at the end of 4 years?

8 0
1 year ago
Brainliest will be given!!
Aleks [24]

Answer:

2nd Option

5th Option

Step-by-step explanation:

Linear equations are defined as functions that have a <em>x</em> term.

Quadratic equations are defined as functions that have a x² term.

Cubic equations are defined as functions that have a x³ term.

4 0
3 years ago
Read 2 more answers
Other questions:
  • What is the unit price if a dozen rolls cost 3.99?
    7·1 answer
  • The first term of an arithmetic progression is -3 and the common difference is 8. What is the 28th term?
    11·1 answer
  • Using the polygon angle sum theorem, find x in the graphic above
    14·1 answer
  • Round 43,846 to the nearest thousand.
    6·2 answers
  • Trigonometry, IF answer is delivered on time WILL give BRANLIEST
    11·1 answer
  • In a sale, all normal prices are reduced by 15%
    15·1 answer
  • In medical experiments, half of the participants are given the medication, and the remaining participants are given a placebo. A
    11·1 answer
  • Identify the value of x that makes each pair of ratios equivalent.<br> 2:x and 12:18
    13·1 answer
  • Segment addition postulate help
    6·1 answer
  • The cost of having photos taken includes a sitting fee and $12 for each portrait. The cost of 3, 6, and 9 photos respectively is
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!