Question

Good afternoon,

I need a bit of help.
So ive got my first derivative which is

6x^2-6x-12

and the stationary points ive found are x=-1 and x=2 at which points the value of the derivative is zero.

So im attempting to classify the points. From my derivative tests

the value of -2 should give a value of 24 which is positive.
6(-2)^2-6(-2)-12 = 24

and a value of 3 should give 24 also which is again positive.
6(3)^2-6(3)-12 = 24

So I would classify my stationary points as a point of inflection?

Is that correct or did I need to simplify the derivative further before applying this test?

And have I gone wrong at any point along the way that you can see?

Answer 1

You say dy/dx = 6(x^2 - x - 2)

so the function is horizontal when
(x-2)(x+1) = 0
or
x = 2 and x = -1 Agreed
NOW
you can test it like you did, but usually what you do is take the second derivative. If it is +, the function is at the bottom and about to start up. If it is negative, the function is at a hump and about to head down. If it is zero, then inflection point.
so (I am ignoring that 6 we factored out)

d^2y/dx^2 = 2 x - 1
at x = -1 this is
NEGATIVE, so function at a maximum
at x = 2, this is POSITIVE so function is at a minimum and about to head up.