Question
The function $f(x)=\frac{\log x}{x}$ is increasing in the interval(a) $(1,2 e)$(b) $(0, e)$(c) $(2,2 e)$(d) $\left(\frac{1}{e}, 2 e\right)$.
Step 1
We can use the quotient rule for differentiation, which states that the derivative of $\frac{u}{v}$ is $\frac{u'v - uv'}{v^2}$, where $u$ and $v$ are functions of $x$, and $u'$ and $v'$ are their respective derivatives. Show more…
Show all steps
Your feedback will help us improve your experience
Aman Gupta and 51 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
'The function $f(x)=2 \log (x-2)-x^{2}+4 x+1$ increases in the interval (a) $(1,2)$ (b) $(2,3)$ (c) $(5 / 2,3)$ (d) $(2,4)$
The function $f(x)=2 \log (x-2)-x^{2}+4 x+1$ increases on the interval (a) $(1,2)$ (b) $(2,3)$ (c) $\left(\frac{5}{2}, 3\right)$ (d) $(2,4)$
Monotonocity
Level II
The function $f(x)=\frac{x}{\log x}$ increases on the interval (a) $(0, \infty)$ (b) $(0, e)$ (c) $(e, \infty)$ (d) none
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD