find maximum and minimum value of y with graph if y=x/(4+x)^2

Question

we have to find the value of y with graphical representation of maxima and minima

Answer 1

When x=-4 y approaches minus infinity because x=-4 is an asymptote. It's minus infinity rather than plus infinity because the numerator is negative around x=-4, while denominator approaches zero from the positive side. The curve passes through the origin (0,0).

y'=((4+x)^2-2x(4+x))/(4+x)^4; this is zero when the numerator is zero: 4+x=2x, x=4 and y=4/8^2=1/16=0.0625. The point (4,1/16) is a maximum. Minus infinity is the minimum.