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trapecia [35]
3 years ago
11

Which function has the graph shown?

Mathematics
1 answer:
Bas_tet [7]3 years ago
7 0
What does the graph look like so I can answer the question, please send a picture of the graph.
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1) Let f(x)=6x+6/x. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relat
brilliants [131]

Answer:

1) increasing on (-∞,-1] ∪ [1,∞), decreasing on [-1,0) ∪ (0,1]

x = -1 is local maximum, x = 1 is local minimum

2) increasing on [1,∞), decreasing on (-∞,0) ∪ (0,1]

x = 1 is absolute minimum

3) increasing on (-∞,0] ∪ [8,∞), decreasing on [0,4) ∪ (4,8]

x = 0 is local maximum, x = 8 is local minimum

4) increasing on [2,∞), decreasing on (-∞,2]

x = 2 is absolute minimum

5) increasing on the interval (0,4/9], decreasing on the interval [4/9,∞)

x = 0 is local minimum, x = 4/9 is absolute maximum

Step-by-step explanation:

To find minima and maxima the of the function, we must take the derivative and equalize it to zero to find the roots.

1) f(x) = 6x + 6/x

f\prime(x) = 6 - 6/x^2 = 0 and x \neq 0

So, the roots are x = -1 and x = 1

The function is increasing on the interval (-∞,-1] ∪ [1,∞)

The function is decreasing on the interval [-1,0) ∪ (0,1]

x = -1 is local maximum, x = 1 is local minimum.

2) f(x)=6-4/x+2/x^2

f\prime(x)=4/x^2-4/x^3=0 and x \neq 0

So the root is x = 1

The function is increasing on the interval [1,∞)

The function is decreasing on the interval (-∞,0) ∪ (0,1]

x = 1 is absolute minimum.

3) f(x) = 8x^2/(x-4)

f\prime(x) = (8x^2-64x)/(x-4)^2=0 and x \neq 4

So the roots are x = 0 and x = 8

The function is increasing on the interval (-∞,0] ∪ [8,∞)

The function is decreasing on the interval [0,4) ∪ (4,8]

x = 0 is local maximum, x = 8 is local minimum.

4) f(x)=6(x-2)^{2/3} +4=0

f\prime(x) = 4/(x-2)^{1/3} has no solution and x = 2 is crtitical point.

The function is increasing on the interval [2,∞)

The function is decreasing on the interval (-∞,2]

x = 2 is absolute minimum.

5) f(x)=8\sqrt x - 6x for x>0

f\prime(x) = (4/\sqrt x)-6 = 0

So the root is x = 4/9

The function is increasing on the interval (0,4/9]

The function is decreasing on the interval [4/9,∞)

x = 0 is local minimum, x = 4/9 is absolute maximum.

5 0
2 years ago
Given the function f(x) = –5|x + 1| + 3, for what values of x is f(x) = –12?
Alexus [3.1K]
The answer to your question is negative 52. hope i helped.
7 0
3 years ago
Read 2 more answers
Which of the following statements is true ? HELLLLP ASSSSAPP TRYAN GRADUATE UKKK
Soloha48 [4]

Answer:

Both are irrational

Step-by-step explanation:

\sqrt{\frac{4}{9} } is a trick as it does simplify to \frac{2}{3} , but that is irrational

4 0
3 years ago
Please help!!!!!!!! Find radius and diameter. will mark brainiest!!!!!!!!!!
mylen [45]

Answer:

The radius is given its 10 in

The diameter is 20 in

Step-by-step explanation:

Two find the diameter given the radius you just multiply by 2

10x2=20 therefore the diameter is 20

Hope this helps :)

8 0
2 years ago
Read 2 more answers
Please help will mark branlist!!
insens350 [35]

Answer:

x=9

Step-by-step explanation:

Looking at the diagram, we see that four angles are formed by the intersection of two lines. The angles highlighted in blue and green are therefore, vertical angles. We know that vertical angles have equal angle measures meaning that in this case, the measure of the blue angle is equal to the measure of the green angle. Using this, we can now solve for x:

7x+49=2x+94

7x-2x=94-49

5x=45

x=45/5

x=9

8 0
3 years ago
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