Draw the graph of y=`(x^(2))/(sqrt(x+1))`

Explanation

we have y =`f(x)=(x^(2))/sqrt(x+1)`
Clearly domain of function is [-1,` 00 `]
`(x^(2))/sqrt(x+1)ge0,forall` x in R.
`therefore`Graph entirely lies above x axis
`underset(xrarr1)lim(x^(2))/sqrt(x+1)=00`
f(0)=0
`f^(prime)(x)=2xsqrt(x+1)-(x^(2))/2sqrt(x+1)/(x+1)`
`=(4x(x+1)-x^(2))/(2(x+1)sqrt(x+1))`
`=(x(3x+4))/(2(x+1)sqrt(x+1)), xgt-1`
`f(x)lt0for-1ltxlt0`,where f(x)decreases
and(x)`gt0forxgt0`,where f(x)increases.
Hence x=0 is point of minima.
`underset(xrarr00)lim(x^(2))/sqrt(x+1)=00`
From the above information the graph of function is as shown in they figure.