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Bingel [31]
3 years ago
12

Which of these equations represent functions? Check all that apply.

Mathematics
1 answer:
AVprozaik [17]3 years ago
5 0
A is quadratic function
B is equation of a circle
C is equation of a line
D is hiperbolic funciotn
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F is a twice differentiable function that is defined for all reals. The value of f "(x) is given for several values of x in the
nadezda [96]

The correct answer is actually the last one.

The second derivative f''(x) gives us information about the concavity of a function: if f''(x) then the function is concave downwards in that point, whereas if f''(x)>0 then the function is concave upwards in that point.

This already shows why the first option is wrong - if the function was concave downwards for all x, then the second derivate would have been negative for all x, which isn't the case, because we have, for example, f''(8)=5

Also, the second derivative gives no information about specific points of the function. Suppose, in fact, that f(x) passes through the origin, so f(0)=0. Now translate the function upwards, for example. we have that f(x)+k doesn't pass through the origin, but the second derivative is always f''(x). So, the second option is wrong as well.

Now, about the last two. The answer you chose would be correct if the exercise was about the first derivative f'(x). In fact, the first derivative gives information about the increasing or decreasing behaviour of the function - positive and negative derivative, respectively. So, if the first derivative is negative before a certain point and positive after that point. It means that the function is decreasing before that point, and increasing after. So, that point is a relative minimum.

But in this exercise we're dealing with second derivative, so we don't have information about the increasing/decreasing behaviour. Instead, we know that the second derivative is negative before zero - which means that the function is concave downwards before zero - and positive after zero - which means that the function is concave upwards after zero.

A point where the function changes its concavity is called a point of inflection, which is the correct answer.

7 0
3 years ago
Part A
kodGreya [7K]
What was the answer?
8 0
3 years ago
Read 2 more answers
Multiply or divide. Show your work.<br><br> 3n²-n/n²-1÷n²/n+1
Ugo [173]
\frac{3n^{2} - n}{n^{2} - 1} \div \frac{n^{2}}{n + 1}
\frac{n(3n) - n(1)}{n^{2} + n - n - 1} \div \frac{n^{2}}{n + 1}
\frac{n(3n - 1)}{n(n) + n(1) - 1(n) - 1(1)} \div \frac{n^{2}}{n + 1}
\frac{n(3n - 1)}{n(n + 1) - 1(n + 1)} \div \frac{n^{2}}{n + 1}
\frac{n(3n - 1)}{(n - 1)(n + 1)} \div \frac{n^{2}}{n + 1}
\frac{n(3n - 1)}{(n - 1)(n + 1)} * \frac{n + 1}{n^{2}}
\frac{3n - 1}{n - 1} * \frac{1}{n}
\frac{3n - 1}{n(n - 1)}

5 0
3 years ago
(WILL GET BRAINLESS IF YOU EXPLAIN)
Vaselesa [24]

Answer:

Quran Surah Fatir 35:5

Step-by-step explanation:

What this verse is trying to say is, don't let this life you are living right now mislead you and misguide you!  For example, you see non-believer doing zina, drinking alchoal, or doing bad sins. These are some of the major distractions and the disbelievers who do these types of stuff will try to mislead you by making you do this also with them.

(I want to clarify it's better if you go to an Imam or somebody knowledgeable and ask them because they will help you explain this verse in a more understandable way. I tried but it's better to check an Imam!)

Hope this helped!

5 0
2 years ago
Which two integers is √56 between?<br> Please help me.
lozanna [386]

Answer:

7 and 8.

Step-by-step explanation:

When we check out what is √49 and √64, we can see that they equal 7 and 8 respectively. Since √56 is between √49 and √64, we can say that √56 is between 7 and 8.

Hoped this helped.

8 0
2 years ago
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