Question

Need Help! Use f(x) = (lnx) / Sqrtx to do the following below:
a) find where its increasing or decreasing
b) find local max and mins values
c) find intervals of concavity and inflection points

Answer 1

Have you started? If so, then jot everything down.

Answer 2

Start by the first derivative test.

Answer 3

\[f(x) = \frac{lnx}{\sqrt{x}}\]

Answer 4

Use quotient rule

Answer 5

and this time I realized my error from earlier.... just setting that f(x) = 0 is equilibrium which is not what we need
so obtain the first derivative and set f'(x) = 0 to solve for critical points
then pick a value between the intervals and plug it into f'(x) to see if it increases or decreases
you will need to obtain the second derivative for concavity f''(x) = 0 and repeat the steps above to see if we have concave up or concave down.

Answer 6

+1 Usukidoll
Also, please post all your work. Posting just the question is not telling us much on what you need help with.

Answer 7

@Zale101 that's what happens when insomnia for weeks plagues my brain... the thinking goes nuts @______@

Answer 8

I understand. It makes it hard for tutors to tutor properly when they dont know what the real problem the tutee is asking. Do they want us to explain everything in the concept? Or is there some certain part of the problem they are confused with?

Answer 9

Oops, didnt see these comments until now. Either way, I also know how to get the first derivative of this

Answer 10

which is: sqrt of x * (1/x) - (lnx) (1/2x^-1/2) all over (sqrt of x) ^2

Answer 11

But I dont know how to go about from there

Answer 12

Find the stationary point, I.E, f'(x)=0. Then check for adjacent points to see if the derivative is increasing or deacreasing nearby.