# [SOLVED]S8. 3.7.10 at which photosynthesis takes place (min/max)

#### karush

##### Well-known member
10. The rate (in mg carbon$/m^3/h$) at which photosynthesis takes place for a species of phytoplankton is modeled by the function

$P=\dfrac{100I}{I^2 + I + 4}$
where I is the light intensity (measured in thousands of foot-candles). For what light intensity is $P$ a maximum?

OK I presume first we derive P'

$P'=\dfrac{ -100 (I^2 - 4)}{(I^2 + I + 4)}^2$

$P'(I)=0$ at $x=\pm 2$

so far !!!

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#### skeeter

##### Well-known member
MHB Math Helper
$P’=\dfrac{100(4-I^2)}{(I^2+I+4)^2}$

does $I =-2$ make sense given what $I$ represents?

So, how do you determine if $I=2$ determines a maximum?

#### karush

##### Well-known member
Can Intensity be negative?

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Can Intensity be negative?

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Can Intensity be negative?