Can you check my answer?

Question

Solve the separable differential equation: dy/dx=(sqrt(x))/2y
y=(2/3)x^(3/4)

Let f be the function given by f(x)=x^3-5x^2+3x+k is a constant.
a) On what intervals is f is increasing? (-oo,1/3), (3,oo)
b) On what intervals is the graph of f concave downward? (-oo,10/9)
c)Find the value of k for which f has 11 as its relative maximum.
I am not sure on this one. Here is what I think I would start this one:
11=x^3-5x^2+3x+k What would I plug in for x?