root function analysis

**natanson.meital** · February 6th 2008, 05:39 AM

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.
Please help us to finish the question.
Thanks.

**CaptainBlack** · February 6th 2008, 10:19 PM

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.
Please help us to finish the question.
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

Thread: root function analysis

LinkBack

Thread Tools

Display

root function analysis

Similar Math Help Forum Discussions

Limit of the nth root of a function

square root function

Complex Analysis Square Root of Z^2

Function and root

Square Root Function

Search Tags