I will assume you meant
y = 9x^(1/2) (e^-x)
dy/dx = 9x^(1/2) (-e^-x) + (e^-x)(9/2)x^(-1/2)
= -(9/2)x^(-1/2) (e^-x)[2x - 1]
= 0 for a max/min of y
if -(9/2)x^(-1/2)=0 we have no solution
if e^-x = 0 we have no solution
if 2x-1 = 0 we get x = 1/2
f(1/2) = 9√(1/2) e^(-1/2) = appr. 3.86
f(x) = 9 sqrt(x)e*(-x)
1 answer