Page 161 - How To Solve Word Problems In Calculus

6. Let x be the distance Lindsay stands from the wall.

3

α
θ 1
β
x

5

x

4 1
Let α and β be as shown. tan α = and β = . Since θ = α − β,
x x

tan θ = tan(α − β)
tan α − tan β
=
1 + tan α tan β
4 1
−
x x
=
4
1 +
x 2
3
x
=
4
1 +
x 2
3x
tan θ =
2
x + 4
dθ
Since we want to minimize θ, we need . Differentiating with
dx
respect to x,

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