Maggie is training to run a 6 mile race. Her training program has her increase her weekly long run each week. This week she ran
1 answer:
Answer:
Maggie will run 5.85 miles next week.
Step-by-step explanation:
Given:
Maggie is training to run a 6 mile race.
This week Maggie ran = 4.5 miles
Also Given:
Next week she will run 1.3 times as far as she did this week.
We need to distance she will run next week.
Now we know Next week she will run 1.3 times as far as she did this week.
It means Distance to be run next week will be equal to 1.3 times distance she ran this week.
Framing in equation form we get;
distance she will run next week =
Hence Maggie will run 5.85 miles next week.
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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.