Question

Maximize the Yield (see attachment)

Answer 1

so i should probably take the limit?

Answer 2

find the derivative,
set it equal to 0 and find ur critical points ?

Answer 3

i presume u knw optimization as i saw u doing integrals in ur past posts

Answer 4

Im still working the numbers, I'm missing something for sure..

Answer 5

did u find the derivative ?

Answer 6

\(Y(N) = \dfrac{N}{1+N^2}\)

\(Y'(N) = ?\)

Answer 7

yeah i got (N)(-1)(1+N)^(-2) + (1+N)^-1

Answer 8

one sec leme check

Answer 9

uhg i know what i did, i took y'(n) or (1+N)^-1 instead of -2 power

Answer 10

of*

Answer 11

hahah try again

Answer 12

use quotient/product rule whichever you're friendly wid

Answer 13

so i got N = 1

Answer 14

after setting my new derivative to zero

Answer 15

Excellent !

Answer 16

so, N = 1 is your only critical value

Answer 17

so the slope of my graph is zero at x = 1 therefore that is a min or a max

Answer 18

so i need to find if it is increasing or decreasing on either side right?

Answer 19

Yep !

you got it !! it better give a max value as the graph is decreasing (intuitively)

use second derivative to figure out whether its min/max/neither

Answer 20

find second derivative,
evaluate it at 1

Answer 21

f''(1) is negative => its a max

Answer 22

it is so Nitrogen level 1 maximizes the yield

Answer 23

thank you :)

Answer 24

Correct ! graph it and see for double confirmation :)

Answer 25

yeah ill graph it now, i was trying to do it without, and we did :D

Answer 26

WFA sometimes prevents me from learning

Answer 27

lol true, WFA's job is to check ur answers... i bet you're wise enough to cheat urself :P