(15x-24x+9) divided by(3x-3)
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for the implicit integration I got:
the vertical tangent would at points at which y' goes to infinity.
that happen when the right-hand side has singularities, that is, the denominator is 0:
so the two points y above have a vertical tangent.
First of all, I'm going to assume that we have a concave down parabola, because the stream of water is subjected to gravity.
If we need the vertex to be at , the equation will contain a
term.
If we start with we have a parabola, concave down, with vertex at
and a maximum of 0.
So, if we add 7, we will translate the function vertically up 7 units, so that the new maximum will be
We have
Now we only have to fix the fact that this parabola doesn't land at , because our parabola is too "narrow". We can work on that by multiplying the squared parenthesis by a certain coefficient: we want
such that:
- when we plug
, we have
Plugging these values gets us
As you can see in the attached figure, the parabola we get satisfies all the requests.
