# Math Help - root function analysis

1. ## root function analysis

Here is the function $y=x*sqrt[a+b*x^2]$
the tangent equation of the function at $x=sqrt[5]$
is $x+2y=5*sqrt[5]$

A. Find a and b.
B. Find the function definition range.
C. Find the minimum & maximum points.

We tried to derive the function but we didn't succeed.
Thanks.

2. Originally Posted by natanson.meital
Here is the function $y=x*sqrt[a+b*x^2]$
the tangent equation of the function at $x=sqrt[5]$
is $x+2y=5*sqrt[5]$

A. Find a and b.
B. Find the function definition range.
C. Find the minimum & maximum points.

We tried to derive the function but we didn't succeed.
Thanks.
When $x=\sqrt{5}$ we have from the original equation:

$y=\sqrt{5} \sqrt{a+5b}$

and from the tangent equation:

$y=2 \sqrt{5}$

so:

$a+5b= 4$

You obtain the second equation that you need by equating derivatives of the
original equation and tangent at $x=\sqrt{5}$, which I will leave to you.

RonL