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Answer:
a) , b)
.
Step-by-step explanation:
a) The graphic is enclosed to the problem. By visual inspection, an absolute maximum is found.
b) The exact method consists in the application of the First and Second Derivative Tests. First and second derivatives are, respectively:
The First Derivative Test consists in equalizing the first derivative to zero and solving the expression:
According to the second derivative, the critical point leads to a maximum. The remaining component is determined by evaluation the polynomial:
The exact solution is , indicating that graphic solution leads to a good approximation.
Answer:
<u>60</u> students are involved in either band or sports.
<u>95</u> students are not involved in either sports or band.
Step-by-step explanation:
Given:
In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students participate in both activities.
Now, to find the students are involved in either sports or band. And students who are not involved in either sports or band.
<em>Total number of students</em> = 320.
Number of students in the band = 85.
Number of students in the sports team = 200.
Number of students participate in both activities = 60.
Thus, 60 students are involved in either band or sports.
So, the number of students in the band adding number of students in the sports team we get:
200 + 85 = 285.
Then, to subtract the number of students participate in both activities we get:
285 - 60 = 225.
<em>Thus, the remaining students are </em>= 225.
Now, to get the students who are not involved in either sports or band we subtract the total number of students from the remaining students:
Therefore, 60 students are not involved in either band or sports. 95 students are not involved in either sports or band.