How to solve for x ?

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- February 26th 2006, 12:32 AMtotalnewbieSolve for x
How to solve for x ?

- February 26th 2006, 04:06 AMCaptainBlackQuote:

Originally Posted by**totalnewbie**

real (sketch the curve for to see why).

Problem was: Solve

RonL - February 26th 2006, 04:57 AMtotalnewbie
It seems to me that I have lost. My goal was to find common tangent for two functions: f(x)=x^2/2e and g(x)=ln(x)

It was also said that x-coordinate is sqrt(e^1) for one tangent point. - February 26th 2006, 05:24 AMCaptainBlackQuote:

Originally Posted by**totalnewbie**

Trial 1

Assume the point is the tangency point on

Then we can find the slope of the tangent at , and

the corresponding value of , which will allow us to find

the equation of the tangent. Now check that this line is a tangent

to , if it is our job is done, if not proceed to Trial 2

Trial 2

Assume the point is the tangency point on ,

then proceed as in Trial 1, but with the roles of and

interchanged.

RonL - February 26th 2006, 07:06 AMtotalnewbie
I have tried it.

The green line doesn't touch the red parabola. But it should touch. - February 26th 2006, 07:12 AMearbothQuote:

Originally Posted by**totalnewbie**

if there exists a common tangent then the gradient of both functions must be equal. So first calculate the drivative of both functions:

Both are equal:

Solve for x and you'll get:

Complete the coordinates:

That means that the graphs of both functions have one common point: the tangent point. There exists one tangent (that's a special case, normally there must be two tangents!)

Use the point-slope-formula:

I've attached a drawing to demonstrate my results.

Greetings

EB - February 26th 2006, 07:20 AMearbothQuote:

Originally Posted by**totalnewbie**

you have typed the function f like this: x^2/2e. Then your computer will calculate .

You have to use parantheses:

Good luck.

Greetings

EB - February 26th 2006, 08:41 AMCaptainBlackQuote:

Originally Posted by**totalnewbie**

RonL