Question

For each interval use the figure (attached below) to choose the statement that gives the location of the global maximum and minimum of f on the given interval.

I) Maximum at right endpoint, minimum at left endpoint
II) Maximum at right endpoint, minimum at critical point
III) Maximum at left endpoint, minimum at right endpoint.
IV) Maximum at left endpoint, minimum at critical point

(Questions below.)

Answer 1

a) The statement that gives the location of the global maximum and global minimum of f on the interval \[4le x \le12\] is _____

b) The statement that gives the location of the global maximum of f on the interval \[11\le x \le16 \] is ______

c) The statement that gives the location of the global maximum and global minimum of f on the interval \[4\le x \le 9\] is _____

d) The statement that give the location of the global maximum and global minimum of f on the interval \[8 \le x \le 18\] is ______

Answer 2

a) is suppose to be \[4 \le x \le 12\]

Answer 3

From the graph, the global minimum of the function is at x = 10 (which is the critical point)
The interval 4 <= x <= 12, includes x = 10. So the global minimum is at the critical point.
To find the global maximum, read the graph at x = 4 and at x = 12 and see which one is higher. f(4) > f(12).
Therefore, in the interval [4, 12], global maximum at left end point and global minimum at the critical point or IV)

Do similar analysis for the other intervals.

Answer 4

Okay, let me see if I got the rest right.

b) f(11) < f(16) --- [16,11] --- (II)
c) f(4) > f(9) --- [4,9] --- (IV)
d) f(8) < f(18) --- [18,8] --- (II)

Answer 5

When specifying intervals make sure the smaller number is on the left and the bigger number is on the right. [11, 16] (and not [16,11].

The interval [11, 16] does NOT include 10 which is the critical point.
You are correct that f(11) < f(16).
So global maximum at right end point and minimum at left end point. So (I)

Answer 6

Your answer to d) is correct but not to c) because the interval [4,9] excludes the critical point which is at x = 10 and so critical point should not be in the answer.

Answer 7

Alright, thanks for explaining that to me ^^!