so

and

For a point of inflection,

So at (origin)

.

Now at (2,4) as we have a local maximum, and we must make sure so it is a max and not a min.

Substituting in the values:

(b is gone as it equals zero)

Now, we know that

We know that at , , so you can see .

Now we get .

You know that at , . Simply substitute these values into the equation to find a. Then you can find c.