f(x) = 1/y: properties

[Jack]

Hi,
It's been a while, if anyone is still here...
I just need a run-down of the properties for the curve for f(x)=1/y for
y >0. I need to be able to say in good mathematical language the values
of x and y at which its slope is at 45%; and how to say that it gets
ever straighter as you move along the x-axis from this point.
With thanks in advance.

[Jack]

Post by Jack
Hi,
It's been a while, if anyone is still here...
I just need a run-down of the properties for the curve for f(x)=1/y for
y >0. I need to be able to say in good mathematical language the values
of x and y at which its slope is at 45%; and how to say that it gets
ever straighter as you move along the x-axis from this point.
With thanks in advance.

And if one were to draw a right-angled triangle, ABC, where C is the
hypotenuse, B is the longer of the two sides and is beneath our curve
and on the x-axis, and the vertices AC and BC intersect with f(x), what
claim can we make about the area, a, beneath the curve but also within
ABC, as regards a/b where b is the area of the triangle? Is it constant
for any specified value of the length of A? Or is it simply constant?

[Jack]

Post by Jack

Post by Jack
Hi,
It's been a while, if anyone is still here...
I just need a run-down of the properties for the curve for f(x)=1/y for
y >0. I need to be able to say in good mathematical language the values
of x and y at which its slope is at 45%; and how to say that it gets
ever straighter as you move along the x-axis from this point.
With thanks in advance.

And if one were to draw a right-angled triangle, ABC, where C is the
hypotenuse, B is the longer of the two sides and is beneath our curve
and on the x-axis, and the vertices AC and BC intersect with f(x), what
claim can we make about the area, a, beneath the curve but also within
ABC, as regards a/b where b is the area of the triangle? Is it constant
for any specified value of the length of A?

<< Or is it simply constant?>>

Oh I can see that this isn't true.