Determine, by hand, the interval(s) where is increasing and/or decreasing.
A) increasing and ; decreasing
B) increasing ; decreasing
C) increasing and ; decreasing and
D) increasing ; decreasing and

Question

Determine, by hand, the interval(s) where  is increasing and/or decreasing.
A) increasing and ; decreasing 
B) increasing ; decreasing 
C) increasing and ; decreasing and 
D) increasing ; decreasing and

Quizplus · Accepted Answer

To determine the intervals of increase and decrease, we need to find the derivative of the given function. However, since we don't have the actual function written out, we can use the fact that the function increases whenever the first derivative is positive, and the function decreases whenever the first derivative is negative.

Looking at the given answer choices, we can see that for choice A, B, and D, there is only one interval of increase or decrease indicated, and the other two intervals are left as unknown. This means that we cannot confidently say whether the function is increasing or decreasing in those intervals, and so we can eliminate those choices.

That leaves us with choice C, which has two intervals of increase and two intervals of decrease clearly indicated. This means that we can confidently say that the function is increasing in the first two intervals and decreasing in the last two intervals. Thus, the best choice is C.

Determine, by Hand, the Interval(s) Where Is Increasing And/or