# root function analysis

• Feb 6th 2008, 05:39 AM
natanson.meital
root function analysis
Here is the function $\displaystyle y=x*sqrt[a+b*x^2]$
the tangent equation of the function at $\displaystyle x=sqrt[5]$
is $\displaystyle x+2y=5*sqrt[5]$

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.
• Feb 6th 2008, 10:19 PM
CaptainBlack
Quote:

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

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 $\displaystyle x=\sqrt{5}$ we have from the original equation:

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

and from the tangent equation:

$\displaystyle y=2 \sqrt{5}$

so:

$\displaystyle a+5b= 4$

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

RonL