If f(x)  be a real valued function, f(x)+f(x+4)=f(x+2)+f(x+6),g(x)=∫xx+8f(t)dt . Then g'(x)  is equal to

∵f(x)+f(x+4)=f(x+2)+f(x+6)  ….(i)Replacing x by x+2 in Eq. (i), thenf(x+2)+f(x+6)=f(x+4)+f(x+8), ….(ii)From eqs. (i) and (ii) we getf(x+8)=f(x)⇒f(x+8)−f(x)=0   …….(iii)Now, g(x)=∫xx+8f(t)dt∴g'(x)=f(x+8)−f(x)   [from eq.(iii)]=0