Consider the equation below. f(x) = x^7 lnx Find the interval on which f is increasing. Find the interval on which f is decreasing. Consider the equation below. f(x) = x^7 ln x (Enter your answer...
Consider the equation below. f(x) = x^7 lnx
Find the interval on which f is increasing.
Find the interval on which f is decreasing.
Consider the equation below. f(x) = x^7 ln x
(Enter your answer using interval notation.)
- print Print
- list Cite
Expert Answers
calendarEducator since 2012
write738 answers
starTop subjects are Math and Science
If you have more than one question, you need to make separate posts.
To find where a function is increasing and decreasing, you need to find where the derivative of the function is greater than zero or less than zero.
`f(x)=x^7lnx` differentiate using product rule
`f'(x)=7x^6lnx+x^7/x`
`=x^6(7lnx+1)`
Since `x^6` is always positive, we need to determine when `7lnx+1` is greater than zero or less than zero. We first find when it is equal to zero, then it will be positive on one side and negative on the other.
`7lnx+1=0`
`7lnx=-1`
`lnx=-1/7` switch to exponential form
`x=e^{-1/7}`
This means that when `(e^{-1/7},infty)` , then the derivative is positive, which means the function is increasing, and when `(0,e^{-1/7})` , the derivative is negative, which means the function is decreasing.
Related Questions
- Consider the equation below.Consider the equation below. f(x)= e^(5x) + e^(−x) Find the...
- 1 Educator Answer
- CalculusConsider the equation below. f(x) = e^(3x) + e^(−x) (a) Find the intervals on which f...
- 1 Educator Answer
- f(x)= ln(1-ln(x)) a) indicate where f(x) is decreasing using interval notation b)Use interval...
- 1 Educator Answer
- Solve the logarithmic equation lnx - ln(x+1) = 2?
- 1 Educator Answer
- `f(x) = (x^2) - x - ln(x)` (a) Find the intervals on which `f` is increasing or decreasing....
- 2 Educator Answers
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.