"A fence 1.5m high and is 1m from a wall. A ladder must start from the ground, touch the top of the fence, and rest somewhere on the wall, calculate minimum length of the ladder."

I did y = 1.5x / (x-1)

I used the formula L = sqrt(x^2 + ((1.5x)/(x-1))^2)

My derivative (the top half) turned out to be:

$\displaystyle 0 = 2x (1 - \frac{-4.5x}{(x-1)^3})$

I got 2 solutions, x = 0 or x =~2.3104. A derivative calculator confirmed this.

when going back to my original equation, y = 1.5x / (x-1) I get y = 2.644

dong sqrt(2.644^2 + 2.3104^2) gives me an answer of ~3.5

The book says the answer is 4.5.

Can anyone provide any insight? Thanks.