What value of x maximizes F when Solution rather integrating it first and then using derivative simply use Leibnitz rule here of differentiation 1/[(x+4)2 + 3] - 1/[x2 + 3] put value of upper limitin integrand and multipy it with diferentiation of upper limit w.r.t variable \'x\' minus , put value of lower limit in integrand multiply by differntaition of lower limit w.r.t variable \'x\' as written above expression (x2 + 3) - (x+4)2 - 3 = 0 -16 - 8x = 0 x = -2 answer !!!! you can check whether it is maximum or minimum at x =-2 using second derivative I am not doing it here ......

1. What value of x maximizes F when
Solution
rather integrating it first and then using derivative
simply use Leibnitz rule here of differentiation
1/[(x+4)2 + 3] - 1/[x2 + 3]
put value of upper limitin integrand and multipy it with diferentiation of upper limit w.r.t
variable 'x'
minus , put value of lower limit in integrand multiply by differntaition of lower limit w.r.t
variable 'x'
as written above expression
(x2 + 3) - (x+4)2 - 3 = 0
-16 - 8x = 0
x = -2 answer !!!!
you can check whether it is maximum or minimum at x =-2 using second derivative
I am not doing it here .....