Thread: finding the stationary points?

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.

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


Yes you're right. Here's the graph. You can see it yourself in this graph given below.



Hope this helps.