(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.