Question

lnx/x solution extreme value

Answer 1

Answer:

please follow  and following

Answer 2

Answer:

hello there

Step-by-step explanation:

hey dear Here is your answer..

Best Answer

f(x) = (lnx)/x

f'(x) = ((1/x)x - ln(x))/(x^2)

= (1 - ln(x))/(x^2)

0 = (1 - ln(x))/(x^2)

0 = 1 - ln(x), x ≠ 0

ln(x) = 1

e^(ln(x)) = e^1

x = e

Now, to make sure that the maximum occurs at this point, plug values less than and greater than e into f'(x). If a max occurs at x = e, then f'(x<e) will be positive and f'(x>e) will be negative.

f'(1) = (1 - ln(1))/(1^2) = (1 - 0)/1 = 1 ==> positive

f'(e^2) = (1 - ln(e^2))/(e^4) = (1 - 2)/(e^4) = -1/(e^4) ==> negative

So a maximum does occur at x = e. Now, to find the maximum value, find f(e):

f(e) = ln(e)/e = 1/e

So the maximum value is 1/e.

plz it's Mark as brainliest..