MHB What is the Absolute Minimum Value of f(x)?

[karush]

Let f be the function defined by
$f(x)=\dfrac{\ln x}{x}$ What is the absolute minimum value of f
a, 1
b. $\dfrac{1}{e}$
c. 0
d. e
e. none

ok I assume we take the derivative and then set it to zero

$\frac{1-\ln\left(x\right)}{x^{2}}=0$
$x=e$

 

[skeeter]

ok I assume we take the derivative and then set it to zero

then set that into f(x)

I think it is (B)

how do you know it’s not a minimum?

 

[HallsofIvy]

ok I assume we take the derivative and then set it to zero

then set that into f(x)

I think it is (B)

Okay, what do you get when you take the derivative? What x value makes that equal to 0? In other words, tell us why you "think it is (B)!