I am trying to self teach myself calculus and was wondering if someone could tell me I have done this correctly and got the right answer.

find the stationary points of this function:

f(x)=-2x^3-9x^2+24x+40

so the deriviative is

f '(x)=6(-x^2-3x+4)

The stationary points occur where f '(x)=0

so 6(-x^2-3x+4)=0

so 6(1-x)(x+4)=0

so x-1=0 and x+4=0

x=1 and x=-4

The satatinary points occur when x=1 and x=-4

subsitute back into origanal function and the stationary points are:

(1,53) and (-4,-72)

If someone could confirm if I am right or where I have gone wrong it would be a great help thanks.