ii)
dI/dx > 0 if P<0
both bracketed terms of P are > 0. First one obviously is since all terms>0
for the second bracket
x2 + 64 + 225 - 16.sqrt[289] > 0
x2 + 17*17 - 16*17 > 0
x2 + 17 > 0
is true therefore it is always greater than 0
so P<0 for 2x<0 and P>0 for 2x>0
so brightness is increasing for x<0, decreasing for x>0
iii)
P = 2x(x2+ 260)(x2-60)
this is >0 for x>sqrt.60 or -sqrt.260<x<0
decreasing for x<-sqrt.260 or 0<x<sqrt.60
and stationary at x = 0, sqrt60, -sqrt260
dI/dx > 0 if P<0
both bracketed terms of P are > 0. First one obviously is since all terms>0
for the second bracket
x2 + 64 + 225 - 16.sqrt[289] > 0
x2 + 17*17 - 16*17 > 0
x2 + 17 > 0
is true therefore it is always greater than 0
so P<0 for 2x<0 and P>0 for 2x>0
so brightness is increasing for x<0, decreasing for x>0
iii)
P = 2x(x2+ 260)(x2-60)
this is >0 for x>sqrt.60 or -sqrt.260<x<0
decreasing for x<-sqrt.260 or 0<x<sqrt.60
and stationary at x = 0, sqrt60, -sqrt260
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