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
jonny [76]
3 years ago
7

What is the local minimum value of the function? (Round answer to the nearest hundredth) g(x)=x^4-5x^2+4

Mathematics
2 answers:
Cloud [144]3 years ago
5 0

Answer:

-1.58 and 1.58

Step-by-step explanation:

We can determine the local minimum value using the derivative test. We can take the derivative of the function g(x):

g'(x)= (d/dx)g(x)

g'(x)

=4\cdot(x^3)-10\cdot(x)

We find the x values at which the function is zero:

2\cdot(x)\cdot(2\cdot(x^2)-5)=0

Therefore x=0, x=±√5/2

To find the minimum value we substitue our values x=0 or x=-√5/2 or x=√5/2 into g(x)

g(0)=4

g(-√5/2)=-9

g(√5/2)=-9

Therefore the local minimum is -1.58 and 1.58.

Serhud [2]3 years ago
4 0
The local minimum of function is an argument x for which the first derivative of function g(x) is equal to zero, so:
g'(x)=0
g'(x)=(x^4-5x^2+4)'=4x^3-10x=0
x(4x^2-10)=0
x=0 or 4x^2-10=0
4x^2-10=0 /4
x^2-10/4=0
x^2-5/2=0
[x-sqrt(5/2)][x+sqrt(5/2)]=0

Now we have to check wchich argument gives the minimum value from x=0, x=sqrt(5/2) and x=-sqrt(5/2).
g(0)=4
g(sqrt(5/2))=25/4-5*5/2+4=4-25/4=-9/4
g(-sqrt(5/2))=-9/4
The answer is sqrt(5/2) and -sqrt(5/2).

You might be interested in
Management at a seaside resort is publishing a brochure and wants to include a statement about the proportion of clear days duri
Ymorist [56]

Answer: B. 264

Step-by-step explanation:

Formula to calculate the sample size 'n' , if the prior estimate of the population proportion (p) is available:

n= p(1-p)(\dfrac{z}{E})^2

, where z = Critical z-value corresponds to the given confidence interval

E=  margin of error

Let p be the population proportion of clear days.

As per given , we have

Prior sample size : n= 150

Number of clear days in that sample = 117

Prior estimate of the population proportion of clear days = p=\dfrac{117}{150}

E= 0.05

The critical z-value corresponding to 95% confidence interval = z*= 1.95 (By z-table)

Then, the required sample size will be :

n= \dfrac{117}{150}(1-\dfrac{117}{150})(\dfrac{1.96}{0.05})^2

Simplify ,

n= (0.1716)(39.2)^2

n= 263.687424\approx264

Hence, the sample size necessary to construct this interval =264

Thus the correct option is B. 264

7 0
3 years ago
Completely factored form of xy^3 – x^3y?
Zolol [24]

Answer:

xy(y - x)(y + x)

Step-by-step explanation:

take out a common factor xy from both terms

= xy(y² - x²)

y² - x² is a difference of squares and factors in general as (y - x)(y + x)

Hence

xy³ - x³y = xy(x - y)(x + y)



8 0
3 years ago
Pls help. Which of the following numbers represents
serious [3.7K]

Answer:

89percent

Step-by-step explanation:

i am not good at math but what ever

8 0
3 years ago
Which of the following would affect an employee’s net pay?
Aloiza [94]
The answer is D becoz of the explanations
4 0
2 years ago
Read 2 more answers
Use an iterated integral to find the area of the region bounded by the graphs of the equations.
Goryan [66]

Answer:

use photomath and it will solve ur problem

5 0
3 years ago
Other questions:
  • What is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters? Use 3.1
    8·1 answer
  • Simplify the expression . (x^-4)^-6 A. x^-24 B. x^-10 C. x^10 D. x^24
    7·1 answer
  • Which of the following is the quotient of the rational expressions shown
    14·1 answer
  • Determine if the two two equations have the same solution why or why not??
    14·1 answer
  • Which relation is not a function?
    11·1 answer
  • Which graph represents the function y - 3 = 3/2 (x-4)
    8·1 answer
  • Find the value of variable x. If your answer is not an integer, write it in simplest radical form with the denominator rationali
    13·1 answer
  • Please help me with this​
    7·1 answer
  • Help me on these 2 please
    15·1 answer
  • Find the value of 3x³+2x²-4 at x=2​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!