All categories

3 years ago

Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema.

Mathematics

1 answer:

CaHeK987 [17]3 years ago

8 0

Answer:

The function is maxima at x = 0.

Step-by-step explanation:

the function is

$f(x) = x^4 - 8 x^2 + 3$

Differentiate with respect to x.

$f'(x) = 4x^3 - 16 x\\\\Put f'(x) = 0 \\\\4x(x^2-4)=0\\\\4 x(x +2)(x-2) =0\\\\x = 0, - 2 , 2 Now f''(x) = 12 x^2 - 16 \\\\f''(0) = - 16 = negative \\\\f''(-2) = 12(-2)^2 - 16 = 32\\\\f''(2)=12(2)^2 - 16 = 32$

So, the function is maima at x = 0 .

You might be interested in

Drag the tiles to the correct boxes to complete the pairs. Not all tiles are used.

Sati [7]

Answer:

a) aₙ = 4.(2)^n-1

b) aₙ = 2+3(n-1)

c) aₙ = 3+4(n-1)

d) aₙ = 3.(4)^n-1

Step-by-step explanation:

a) a geometric sequence with first term of 4 and a common ratio of 2

aₙ = ar^n-1

where a is the first term and r is the common ratio

aₙ = 4.(2)^n-1

Comparing with the standard form:

1st term = 4

Common ratio = 2

b) an arithmetic sequence with a first term of 2 and a common difference of 3

The standard form of arithmetic sequence is:

aₙ = a₁ + d(n-1)

where a₁ is the first term and d is the common difference

Given: aₙ = 2+3(n-1)

Comparing with standard equation

First term = 2

Common difference = 3

c) an arithmetic sequence with a first term of 3 and a common difference of 4

The standard form of arithmetic sequence is:

aₙ = a₁ + d(n-1)

where a₁ is the first term and d is the common difference

Given: aₙ = 3+4(n-1)

Comparing with standard equation

First term = 2

Common difference = 3

d) a geometric sequence with first term of 3 and a common ratio of 4

aₙ = ar^n-1

where a is the first term and r is the common ratio

aₙ = 3.(4)^n-1

Comparing with the standard form:

1st term = 3

Common ratio = 4

6 0

4 years ago

The difference of two numbers is 3. Their sum is 13. Find the numbers.

Damm [24]

Answer:

Huh

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Calculate the vertices <br> (x+3, y + 1)

butalik [34]

Answer:

A' (4,4), B' (5,7), C' (9,7)

Step-by-step explanation:

7 0

3 years ago

Help me please!!!<br> Determine whether the given number belongs to each set

nata0808 [166]

The given number $-34\frac{3}{8}$ is not a whole number, It is a Integer and Rational number.

<h3>What are Whole Numbers?</h3>

The complete set of natural number with entity '0' is called whole number.

For example: 0, 1, 2, 3, 4, and so on.

<h3 /><h3>What are Integer ?</h3>

Integers are the real number but they can be positive, negative and zero.

For example: -2, -5, -8, 0, 1, 54, 66 etc.

<h3>What are Rational Numbers?</h3>

Rational numbers are those which have a numerator and denominator.

For example: 2/5 here, 2 is numerator and 5 is denominator.

Here, we have given the number as $-34\frac{3}{8}$

it can be solved using - ( 34 x 8 + 3 ) / 8

now, the number becomes

→ - ( 272 + 3 )/8

→ - 275/8

It is not a whole number, it is a integer and it is a rational number too.

Hence,

The given number $-34\frac{3}{8}$ is not a whole number, It is a Integer and Rational number.

Learn more about " Numbers " from here: brainly.com/question/17429689

#SPJ9

5 0

2 years ago

Confused on this one

DiKsa [7]

Answer:

The other measurement has to be 120 degrees. In other words, the two angles have to add up to 180 degrees. The method for that is same side interior.

Step-by-step explanation:

In same side interior angles, the sum of the two angles has to be 180 degrees. So we know that one of the angles is 60 degrees so we do 180-60=120.

5 0

3 years ago