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.