1 Attachment(s)

Why can I not find the top point of this quadratic equation?

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

Attachment 23730

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?

Re: Why can I not find the top point of this quadratic equation?

Hi!

Quote:

Originally Posted by

**MathIsOhSoHard** 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

Attachment 23730
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:

How did you do that?

Quote:

Originally Posted by

**MathIsOhSoHard** Why am I not getting

? According to my graph, that is the correct value?

You can find out by substituting 1/3 for x

So x=1/3 is a solution of the quadratic equation.

By the way are you sure x=1/3 is the one and only solution?

Re: Why can I not find the top point of this quadratic equation?

Quote:

Originally Posted by

**Quant** By the way are you sure x=1/3 is the one and only solution?

No, there are probably more solutions to it. However I really want to know how to get to 1/3.

Re: Why can I not find the top point of this quadratic equation?

Your quadratic factorises (1+x)(1-3x)=0 So x=1/3 or -1

Re: Why can I not find the top point of this quadratic equation?

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