Given the equation:
I want to find the x-value of the top point of this equation, which as a graph I've found to be
However when I try to find this value, I don't end up with
First I differentiate the equation:
Now I put the differentiated equation equal to 0 and isolate x:
Why am I not getting ? According to my graph, that is the correct value?
There are many ways to get this solutions. One of them:
You need to solve
We devide by -3
We add a zero
Some rearranging
As you know it is (do you know this theoreme? Respectively do you see how we find a and b?)
thus
is the same as
Using this in
leads us to
and so on...
so -1 and 1/3 are the solutions you are looking for