Plz help me find x y and b?

Question

Hi

i'm stuck! could you help me out?!?

y=3x is tangent to f(x)=x(√x)+b

find b and (x,y)

answers: b=4 (4,12)

please show your work

thanks.

i've tried

Answer 1

y = 3x is tangent to curve  

y = x^3/2 + b

slope of tangent to curve at any point is given by

dy/dx  = 3/2 x^1/2

slope of line is 3

3x  = 3/2 x^1/2

x^1/2  = 1/2

x  = 4

y = 3* 4  = 12

sub in eq of curve

12 = 4* 4^1/2 + b

12 = 8+b

b = 4