Verify that the function satisfies the three hypotheses of Rolle's Therorem

Question

on the given interval. Then find all numbers c that satisfy the conclusiton
of Rolle's Theorem. f(x)= x*sqrt(x+6) [-6,0]

f is continuous and differential
f(-6) =-6*sqrt(-6+6) =0
f(0)=0
f(x) = x (x+6^1/2)
f'(x)= (x+6^1/2) + (1/2x +6)^1/2
0=(x+6^1/2) + (1/2x +6)^1/2
x=-2.918
I don't think this is correct so could you please tell me what I did wrong?
Thanks.

f(x)= x*sqrt(x+6)--->

f'(x) = sqrt(x+6) + x/[2sqrt(x+6)]

f'(x) = 0 --->

x = -4