(a) Let a > 0 be a constant. Find all critical points of f (x) = x + a√x.
This is my work so far
f'(x)=1+(a/2)(x^(-1/2))
0=1+(a/2)(x^(-1/2))
-1 = (a/2)(1/sqrt(x))
-1=a/(2sqrt(x))
(2)(-1)=(a/(2sqrt(x)))(2)
-2=a/sqrtx
(a)-1/2=sqrtx/a (a)
-a/2=sqrtx
(-a/2)^2=(sqrtx)^2
a/4=x
I calculated the Critical point as x=a/4
(b) Use derivatives to show that f is increasing and its graph is concave down for all x > 0.
Not sure how to do this part.