The band will play for 60 minutes. If the members want to play 5 equal length, how many seconds will each song have to be?
1 answer:
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Answer:
So, its better to buy larger bag
Step By Step Explanation:
Let
Smaller bag hold = x ounces
Price of x ounce in smaller bag = $ y
Price of 1 ounce in smaller bag = ....(1
Larger bag will hold = x + 10 ounces
Price of x+10 ounces in larger bag = y + 1.5
Price of 1 ounce in larger bag = ...(2
Now equation 1 tells that 1 ounce in smaller costs , and equation 2 tells in ounce in larger bag costs
.
Now as we can see, we can get equation 2 from equation 1 by increasing numerator by 1.5 and denominator by 10. In this case denominator has increased more than numerator so the value of overall fraction would be less than
. It means our larger bag has less price per ounce.
So, its better to buy larger bag
The correct answer is actually the last one.
The second derivative gives us information about the concavity of a function: if
then the function is concave downwards in that point, whereas if
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,
Also, the second derivative gives no information about specific points of the function. Suppose, in fact, that passes through the origin, so
. Now translate the function upwards, for example. we have that
doesn't pass through the origin, but the second derivative is always
. 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 . 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.