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timurjin [86]
3 years ago
15

What's the tool that helps you create a perfect circle caleed?

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
4 0
You can draw perfect circles with 
a compass tool
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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
What percent of 7.5 is 0.9
Rina8888 [55]

Answer:

12%

Step-by-step explanation:

0.9/7.5 *100

= 12%

3 0
4 years ago
Based on context clues, which of these words represents the best definition for the underlined word?
kondaur [170]

Answer:

C

Step-by-step explanation:

8 0
3 years ago
Solve it : x² *dy/dx = -2y
zhenek [66]

Answer:

r= -sec(θ) x ∛2

θ=0

Step-by-step explanation:

5 0
3 years ago
Which functions are symmetric with respect to the origin?
Damm [24]

Answer:

The correct option is;

y = arcsinx and y = arctanx

Step-by-step explanation:

The given options are;

1) y = arcsinx and y = arccosx

Here, we have at the origin, where x = 0,  arccosx ≈ 1.57 while arcsinx = 0

Therefore arccosx does not intersect arcsinx at the origin for it to be symmetrical to arcsinx or the origin

2)  y = arccosxy and y = arctanx

Here arctanx = 0 when x = 0 and arcos x = 1.57 when x = 0 therefore, they are not symmetrical

3) y = arctanx and y = arccotx

Similarly, At x = 0, arccotx = 1.57 therefore, they are not symmetrical

4) y = arcsinx and y = arctanx

Both functions arcsinx and arctanx pass through the origin and their shapes are similar but inverted as they go from negative to positive.

3 0
3 years ago
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