Ladder Word Problem Using Local Extrema

[guitarguy]

I am having difficulty with a word problem.

An eight foot fence is placed one foot from a wall. A ladder is placed on the ground, touching the fence and against the wall. What is the shortest ladder that can be placed in this manner?

I set the distance along the ground from the bottom of the fence to the bottom of the ladder as "x".

I set the distance along the ground from the bottom of the wall to the bottom of the ladder as "x+1".

I set the distance from the ground up to the top of fence as "8".

I set the distance from the top of the fence to where the ladder touches the wall as "y".

I see that 8+y divided by x+1 equals 8 divided by x. I solved for y and plugged into the Pythagorean Equation to find the length of the ladder. I got a very long equation wich seems wrong.

I want to differentiate and set equal to zero to find the minimum ladder length.

I am stuck, have tried problem afew times.

Thanks for your help.

 

[tkhunny]

I solved for y

What was the result of this solving?

into the Pythagorean Equation

What was the nature of this equation?

a very long equation wich seems wrong.

What "seems" wrong about it? It is or it isn't. Prove it!

I want to differentiate and set equal to zero to find the minimum ladder length.

Differentiate what? Are you sure you will find a minimum and not a maximum?

 

[guitarguy]

Problem Solved

Thank you for your helpful questions. I thought it over and was able to solve the problem.

The ladder turns out to be 5* sqrt(5) long.

The horrendously long equation for the derivative turned out to be right and required some manipulation to get (x^3-64)(x+1)=0. x=4,-1

Setting the derivative equal to zero worked because I was lookng for a minimum.

Thanks again.