Stationary points - Just checking my working out

Hi guys,
Just wondrered if someone could check i'm on the right track with my woking out on this question as I don't want to progress and mess up the remainder of the question.

Findin the stationary points.
f(x) = -x^3 + 9x^2 - 15x - 10
f'(x) = -3x2 + 18x -15
I have then divided by three to get,
f'(x) = -x^2 +6x -5
0 = -x^2 +6x -5
x^2 -6x +5 = 0
(x-5)(x-1) = 0

Therefore, stationary points are, x = 5 and x = 1.

Thanks.

Although your results are correct, there is a flaw in your logic.

f'(x) = -3x2 + 18x -15

For a stationary point this equals zero, and we have 0 = -3x2 + 18x -15

Now you can divide by 3.

But you can't just divide f'(x) by 3 and claim it's still f'(x)

Ok that makes sense. Thanks for your help

Also if you are asked to find the stationary points you need to give the y value as well as the x