C2 Differentiation, pls help!

Hey, I keep getting the wrong answer for this question, taken from the C2 book (pg. 134, ex. 9B)…it’s number 3g: Find the coordinates of the points where the gradient is zero on the curves with equation y=3* sqrt x (not small 3 inside x, but 3*sqrtx). Establish whether these points are maximum, minimum or points of inflexion, by considering the second derivative.

Also, number 5: By considering the gradient on either side of the stationary point on the curve y=x^3-3x^2+3x, show that this point is a point of inflexion. (And then sketch the curve y=x^3-3x^2+3x)

y=3rtx has no stationary points ?

Question 5,
dy/dx = 3x^2 - 6x + 3
0 = 3x^2 - 6x + 3
0=x^2 - 2x + 1 = (x-1)^2 => x=0 is a stationary point.
When x=0.1, y=0.271
When x = -0.1, y = -0.331
Because its negative one side of the stationary point, and positve the other, it must be a point of inflection.

Plot y = 3x^1/2 and you'll see it doesn't.

You typed
"y=3* sqrt x" I've not got the book here

Oh. And isn't it y=x-3x^1/2?

y=x-3x^1/2
dy/dx = 1-1.5/x^1/2
0 = 1-1.5/x^1/2
1= 1.5/x^0.5
x^0.5 = 1.5
x = 2.25
d^2/dx^2 = 0.75x^-(3/2)
substituing x=2.25, gives d^2/dx^2 = 0.22222 > 0 => minimum