12Find the absolute maximum value on (0, co) for f(x) = 18-12x-XSelect the correct choice below and, if necessary, fill in the answer boxes to complete your choice.at x-O A. The absolute maximum isO B. There is no absolute maximum.lirmIravClick to select and enter your answer(s) and then click Check Answer.rarAll parts showingClear Allhere to search

Question
Asked Nov 11, 2019
21 views
12
Find the absolute maximum value on (0, co) for f(x) = 18-12x-
X
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
at x-
O A. The absolute maximum is
O B. There is no absolute maximum.
li
rm
Irav
Click to select and enter your answer(s) and then click Check Answer.
rar
All parts showing
Clear All
here to search
help_outline

Image Transcriptionclose

12 Find the absolute maximum value on (0, co) for f(x) = 18-12x- X Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. at x- O A. The absolute maximum is O B. There is no absolute maximum. li rm Irav Click to select and enter your answer(s) and then click Check Answer. rar All parts showing Clear All here to search

fullscreen
check_circle

Expert Answer

star
star
star
star
star
1 Rating
Step 1

f(x) = 18 - 12x - 12/x

f'(x) = -12 + 12 / x2

 

Step 2

The critical points are given by f'(x) = -12 + 12 / x2 = 0

Hence,  12 / x2 = 12

Hence, x2 = 1

Hence, x = 1 or -1

However the given interval for x is (0, ∞)

x = -1 falls outside this interval, hence  x = 1 is the only critical point in the given interval.

Step 3
Hence the critical point is x = 1 and the end points of the interval are x = 0 and 
 
f(0) = 18 - 12 x 0 - 12 / 0 = -∞
 
f(1) = 18 - 12 x 1 - 12 / 1 = -6
 
f(∞) = 18 - 12 x ∞ - 12 / ∞ = -∞
 
Since, f(1) is the highest value, hence, the absolute maxima occurs at x = 1 and the maxima is -6
 
...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative