You buy a new pair of shoes that cost $75. The sale tax rate is 8%.

If g is a differentiable function such that g(x)<0 for all real numbers x and if f'(x) = (x2 - 4)g(x), which of the following

galina1969 [7]

We want to see what can we say about f(x) extremes for the given information. We will see that the correct option is:

V: f has a relative minimum at x=-2 and a relative maximum at x=2.

<h3>Maximums and minimums.</h3>

A given function f(x) will have a maximum/minimum at x₀ if:

f'(x₀) = 0

It will be a maximum if f''(x₀) < 0
It will be a minimum if f''(x₀) > 0.

Here we do know that:

f'(x) = (x^2 - 4)*g(x)
g(x) < 0 for all numbers x.

Then the only zeros of f'(x) are when (x^2 - 4) = 0.

And this happens for x = 2 and x = -2

Now let's see if these are minimums or maximums, we have:

f''(x) = 2*x*g(x) + (x^2 - 4)*g'(x)

If we evaluate this in x = 2, we get:

f''(2) = 2*2*g(2) + (2^2 - 4)*g'(2)

= 4*g(2) + 0*g'(2) = 4*g(2)

And g(x) is always negative, then 4*g(2) < 0, then:

f''(2) < 0

Meaning that in x = 2 we have a relative maximum.

For x = -2 we have:

f''(-2) = 2*-2*g(-2) + ((-2)^2 - 4)*g'(-2)

= -4*g(2) > 0

Then f''(-2) > 0, meaning that in x = -2 we have a relative minimum.

Then the correct option is:

V: f has a relative minimum at x=-2 and a relative maximum at x=2.

If you want to learn more about maximums and minimums, you can read:

brainly.com/question/1938915

6 0

2 years ago

When you divide any number by a fraction less than one what happens to the original number

mash [69]

I'm not quite sure, you should be able to divide the original number by 1

5 0

3 years ago

the equation y= - 5.131x2+ 31.821x - 3.333 approximates the number of people standing in line to catch a commuter train x hours

ehidna [41]

We are given function: y= $- 5.131x^2+ 31.821x - 3.333$

Where, x is the number of hours after 5a.m.

We need to approximates the number of people standing in line to catch a commuter train at 7 a.m.

From 5 a.m. to 7 a.m. total number of hours = 7-5 = 2 hours.

So, we need to plug x=2 in the given function.

Plugging x=2 in $y=- 5.131x^2+ 31.821x - 3.333$ , we get

$y=- 5.131(2)^2+ 31.821(2) - 3.333$

Let us simplify it now.

2^2= 4.

Therefore,

$y=- 5.131(4)+ 31.821(2) - 3.333$

= -20.524 + 63.642 - 3.333.

= 39.785 or 40 approximately.

Therefore, the number of people in line at 7 a.m. is approximately 40 people.

Option D.40 is correct option.

3 0

3 years ago

The scatter plot shows the relationship between the test scores of a group of students and the number of hours they exercise in

Y_Kistochka [10]

Answer: Part A: Group p is called a cluster. Group T is called an outlier.

Part B: it seems that as the hours of exercise increases, their test scores increases.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Simplify (6x^-2)^2 (0.5x)^4 Show your work<br> PLEASE HELP THANK YOU!

goldenfox [79]

Use Multiplication Distribute Property: (xy)^a = x^ay^a

6^2(x^-2)^2(0.5x)^4

Simplify 6^2 to 36

36(x^-2)^2(0.5x)^4

Use this rule: (x^a)^b = x^ab

36x^-4(0.5x)^4

Use the Negative Power Rule: x^-a = 1/x^a

36 × 1/x^4(0.5x)^4

Use the Multiplication Distributive Property: (xy)^a = x^ay^a

36 × 1/x^4 × 0.5^4x^4

Simplify 0.5^4 to 0.0625

36 × 1/x^4 × 0.0625x^4

Simplify

2.25x^4/x^4

Cancel x^4

6 0

3 years ago